Publications

Authors Title Journal Abstract

Li-Juan Cheng, Anton Thalmaier & Feng-Yu Wang Covariant Riesz transform on differential forms for $1<p≤2$ Calc. Var. Partial Differential Equations 62 (2023), no. 9, Art. 245, 23 pp

Li-Juan Cheng, Anton Thalmaier & Feng-Yu Wang Some inequalities on Riemannian manifolds linking Entropy, Fisher information, Stein discrepancy and Wasserstein distance Journal of Functional Analysis 285 (2023), no. 5, 109997
Li-Juan Cheng & Anton Thalmaier Dimension-free Harnack inequalities for conjugate heat equations and their applications to geometric flows Analysis & PDE 16 (2023), no. 7, 1589-1620

Qin-Qian Chen, Li-Juan Cheng & Anton Thalmaier Bismut-Stroock Hessian formulas and local Hessian estimates for heat semigroups and harmonic functions on Riemannian manifolds Stochastics and Partial Differential Equations 11 (2023), no. 2, 685-713

Li-Juan Cheng, Erlend Grong & Anton Thalmaier Functional inequalities on path space of sub-Riemannian manifolds and applications Nonlinear Analysis 210 (2021), 112387

Li-Juan Cheng, Anton Thalmaier & Shao-Qin Zhang Exponential contraction in Wasserstein distance on static and evolving manifolds Rev. Roumaine Math. Pures Appl. 66 (2021), no. 1, 107-129

Marc Arnaudon, Anton Thalmaier & Feng-Yu Wang Gradient Estimates on Dirichlet and Neumann Eigenfunctions Int. Math. Res. Not. IMRN 2020, no. 20, 7279-7305

Batu Güneysu & Anton Thalmaier Scattering theory without injectivity radius assumptions, and spectral stability for the Ricci flow Ann. Inst. Fourier (Grenoble) 70 (2020), no. 1, 437-456

Fabrice Baudoin, Erlend Grong, Kazumasa Kuwada, Rob Neel & Anton Thalmaier Radial processes for sub-Riemannian Brownian motions and applications Electron. J. Probab. 25 (2020), paper no. 97, 17 pp.

Anton Thalmaier & James Thompson Exponential integrability and exit times of diffusions on sub-Riemannian and metric measure spaces Bernoulli 26 (2020), no. 3, 2202-2225

Fabrice Baudoin, Erlend Grong, Kazumasa Kuwada & Anton Thalmaier Sub-Laplacian comparison theorems on totally geodesic Riemannian foliations Calc. Var. Partial Differential Equations 58 (2019), no. 4, Art. 130, 38 pp

Anton Thalmaier & James Thompson Derivative and divergence formulae for diffusion semigroups Ann. Probab. 47 (2019) no. 2, 743-773

Erlend Grong & Anton Thalmaier Stochastic completeness and gradient representations for sub-Riemannian manifolds Potential Anal. 51 (2019), no. 2, 219-254

Li-Juan Cheng, Anton Thalmaier & James Thompson Functional inequalities on manifolds with non-convex boundary Sci. China Math. 61 (2018), no. 8, 1421-1436

Li-Juan Cheng, Anton Thalmaier & James Thompson Quantitative C1-estimates by Bismut formulae J. Math. Anal. Appl. 465 (2018), no. 2, 803-813

Li-Juan Cheng, Anton Thalmaier & James Thompson Uniform gradient estimates on manifolds with a boundary and applications Anal. Math. Phys. 8 (2018), no. 4, 571-588

Li-Juan Cheng & Anton Thalmaier Evolution systems of measures and semigroups properties on evolving manifolds Electron. J. Probab. 23 (2018), paper no. 20, 27 pp.

Li-Juan Cheng & Anton Thalmaier Spectral gap on Riemannian path space over static and evolving manifolds Journal of Functional Analysis 274 (2018) 959-984

Li-Juan Cheng & Anton Thalmaier Characterization of pinched Ricci curvature by functional inequalities Journal of Geometric Analysis 28 (2018), no. 3, 2312-2345

Anton Thalmaier Geometry of subelliptic diffusions Geometry, Analysis and Dynamics on sub-Riemannian Manifolds, Vol. II. EMS Series of Lectures in Mathematics, pp. 85-169. European Mathematical Society, Zürich, 2016

Erlend Grong & Anton Thalmaier Curvature-dimension inequalities on sub-Riemannian manifolds obtained from Riemannian foliations: Part I Math. Zeitschrift 282 (2016) 99-130

Erlend Grong & Anton Thalmaier Curvature-dimension inequalities on sub-Riemannian manifolds obtained from Riemannian foliations: Part II Math. Zeitschrift 282 (2016) 131-164

Hongxin Guo, Robert Philipowski & Anton Thalmaier On gradient solitons of the Ricci-Harmonic flow Acta Math. Sin. 31 (2015) 1798-1804

Robert Philipowski & Anton Thalmaier Heat equation in vector bundles with time-dependent metric J. Math. Soc. Japan 67 (2015) 1759-1769

Hongxin Guo, Robert Philipowski & Anton Thalmaier Martingales on manifolds with time-dependent connection J. Theoret. Probab. 28 (2015) 1038-1062

Hongxin Guo, Robert Philipowski & Anton Thalmaier An entropy formula for the heat equation on manifolds with time-dependent metric, application to ancient solutions Potential Analysis 42 (2015) 483-497

Hongxin Guo, Robert Philipowski & Anton Thalmaier A stochastic approach to the harmonic map heat flow on manifolds with time-dependent Riemannian metric Stochastic Processes Appl. 124 (2014) 3535-3552

Marc Arnaudon, Anton Thalmaier & Feng-Yu Wang Equivalent Harnack and gradient inequalities for pointwise curvature lower bound Bull. Sci. Math. 138 (2014) 643-655

Hongxin Guo, Robert Philipowski & Anton Thalmaier A note on Chow's entropy functional for the Gauss curvature flow C. R. Acad. Sci. Paris, Sér. I 351 (2013) 833-835

Hongxin Guo, Robert Philipowski & Anton Thalmaier Entropy and lowest eigenvalue on evolving manifolds Pacific J. Math. 264 (2013) 61-82

Marc Arnaudon & Anton Thalmaier Brownian motion and negative curvature Random Walks, Boundaries and Spectra, Progress in Probability, Vol. 64, 145-163, Springer Basel, 2011

Anton Thalmaier & Feng-Yu Wang A stochastic approach to a priori estimates and Liouville theorems for harmonic maps Bull. Sci. Math. 135 (2011) 816-843

Marc Arnaudon, Koléhè Abdoulaye Coulibaly & Anton Thalmaier Horizontal diffusion in C¹ path space Séminaire de Probabilités XLIII, 73-94, Lecture Notes in Mathematics 2006, Springer, 2011

Marc Arnaudon & Anton Thalmaier The differentiation of hypoelliptic diffusion semigroups Illinois J. Math. 54 (2010) 1285-1311

Hélène Airault, Paul Malliavin & Anton Thalmaier Brownian measures on Jordan-Virasoro curves associated to the Weil-Petersson metric Journal of Functional Analysis 259 (2010) 3037-3079

Marc Arnaudon & Anton Thalmaier Li-Yau type gradient estimates and Harnack inequalities by stochastic analysis Advanced Studies in Pure Mathematics 57 (2010) 29-48

Shizan Fang, Dejun Luo & Anton Thalmaier Stochastic differential equations with coefficients in Sobolev spaces Journal of Functional Analysis 259 (2010) 1129-1168

Marc Arnaudon, Anton Thalmaier & Feng-Yu Wang Gradient estimate and Harnack inequality on non-compact Riemannian manifolds Stochastic Processes Appl. 119 (2009) 3653-3670

Marc Arnaudon, Anton Thalmaier & Stefanie Ulsamer Existence of non-trivial harmonic functions on Cartan-Hadamard manifolds of unbounded curvature Math. Zeitschrift 263 (2009) 369-409

Marc Arnaudon, Koléhè Abdoulaye Coulibaly & Anton Thalmaier Brownian motion with respect to a metric depending on time; definition, existence and applications to Ricci flow C. R. Acad. Sci. Paris 346 (2008) 773-778

Marc Arnaudon, Bruce K. Driver & Anton Thalmaier Gradient estimates for positive harmonic functions by stochastic analysis Stochastic Processes Appl. 117 (2007) 202-220

Marc Arnaudon, Anton Thalmaier & Feng-Yu Wang Harnack inequality and heat kernel estimates on manifolds with curvature unbounded below Bull. Sci. Math. 130 (2006) 223-233

Hélène Airault, Paul Malliavin & Anton Thalmaier Canonical Brownian motion on the space of univalent functions and resolution of Beltrami equations by a continuity method along stochastic flows J. Math. Pures Appl. 83 (2004) 955-1018

Ana Bela Cruzeiro, Paul Malliavin & Anton Thalmaier Geometrization of Monte-Carlo numerical analysis of an elliptic operator: strong approximation C. R. Acad. Sci. Paris 338 (2004) 481-486

Anton Thalmaier & Feng-Yu Wang Derivative estimates of semigroups and Riesz transforms on vector bundles Potential Analysis 20 (2004) 105-123

Paul Malliavin & Anton Thalmaier Numerical error for SDE: Asymptotic expansion and hyperdistributions C. R. Acad. Sci. Paris 336 (2003) 851-856

Marc Arnaudon, Holger Plank & Anton Thalmaier A Bismut type formula for the Hessian of heat semigroups C. R. Acad. Sci. Paris 336 (2003) 661-666

Marc Arnaudon & Anton Thalmaier Yang-Mills fields and random holonomy along Brownian bridges Ann. Probab. 31 (2003) 769-790

Emilio Barucci, Paul Malliavin, M.Elvira Mancino, Roberto Renò & Anton Thalmaier The price-volatility feedback rate: an implementable mathematical indicator of market stability Mathematical Finance 13 (2003) 17-35

Marc Arnaudon & Anton Thalmaier Horizontal martingales in vector bundles Séminaire de Probabilités XXXVI, 419-456, Lecture Notes in Mathematics 1801, Springer, 2003

Hélène Airault, Paul Malliavin & Anton Thalmaier Support of Virasoro unitarizing measures C. R. Acad. Sci. Paris 335 (2002) 621-626

Marc Arnaudon, Robert O. Bauer & Anton Thalmaier A probabilistic approach to the Yang-Mills heat equation J. Math. Pures Appl. 81 (2002) 143-166

Bruce K. Driver & Anton Thalmaier Heat equation derivative formulas for vector bundles Journal of Functional Analysis 183 (2001) 42-108

Marc Arnaudon & Anton Thalmaier Bismut type differentiation of semigroups Prob. Theory and Math. Stat. (Vilnius, 1998), 23-32, VSP/TEV, Utrecht and Vilnius, 1999

Marc Arnaudon, Xue-Mei Li & Anton Thalmaier Manifold-valued martingales, changes of probabilities, and smoothness of finely harmonic maps Ann. Inst. H. Poincaré Probab. Statist. 35 (1999) 765-792

Anton Thalmaier Some remarks on the heat flow for functions and forms Electron. Comm. Probab. 3 (1998) 43-49

Marc Arnaudon & Anton Thalmaier Complete lifts of connections and stochastic Jacobi fields J. Math. Pures Appl. 77 (1998) 283-315

Marc Arnaudon & Anton Thalmaier Stability of stochastic differential equations in manifolds Séminaire de Probabilités XXXII, 188-214, Lecture Notes in Mathematics 1686, Springer, 1998

Anton Thalmaier & Feng-Yu Wang Gradient estimates for harmonic functions on regular domains in Riemannian manifolds Journal of Functional Analysis 155 (1998) 109-124

Anton Thalmaier On the differentiation of heat semigroups and Poisson integrals Stochastics and Stochastics Reports 61 (1997) 297-321

Anton Thalmaier Martingales on Riemannian manifolds and the nonlinear heat equation Stochastic Analysis and Applications. Proc. of the Fifth Gregynog Symposium. World Scientific Press, 1996, 429-440

Anton Thalmaier Brownian motion and the formation of singularities in the heat flow for harmonic maps Probab. Theory Relat. Fields 105 (1996) 335-367

Authors	Title	Journal
Li-Juan Cheng, Anton Thalmaier & Feng-Yu Wang	Covariant Riesz transform on differential forms for $1<p≤2$	Calc. Var. Partial Differential Equations 62 (2023), no. 9, Art. 245, 23 pp
Li-Juan Cheng, Anton Thalmaier & Feng-Yu Wang	Some inequalities on Riemannian manifolds linking Entropy, Fisher information, Stein discrepancy and Wasserstein distance	Journal of Functional Analysis 285 (2023), no. 5, 109997
Li-Juan Cheng & Anton Thalmaier	Dimension-free Harnack inequalities for conjugate heat equations and their applications to geometric flows	Analysis & PDE 16 (2023), no. 7, 1589-1620
Qin-Qian Chen, Li-Juan Cheng & Anton Thalmaier	Bismut-Stroock Hessian formulas and local Hessian estimates for heat semigroups and harmonic functions on Riemannian manifolds	Stochastics and Partial Differential Equations 11 (2023), no. 2, 685-713
Li-Juan Cheng, Erlend Grong & Anton Thalmaier	Functional inequalities on path space of sub-Riemannian manifolds and applications	Nonlinear Analysis 210 (2021), 112387
Li-Juan Cheng, Anton Thalmaier & Shao-Qin Zhang	Exponential contraction in Wasserstein distance on static and evolving manifolds	Rev. Roumaine Math. Pures Appl. 66 (2021), no. 1, 107-129
Marc Arnaudon, Anton Thalmaier & Feng-Yu Wang	Gradient Estimates on Dirichlet and Neumann Eigenfunctions	Int. Math. Res. Not. IMRN 2020, no. 20, 7279-7305
Batu Güneysu & Anton Thalmaier	Scattering theory without injectivity radius assumptions, and spectral stability for the Ricci flow	Ann. Inst. Fourier (Grenoble) 70 (2020), no. 1, 437-456
Fabrice Baudoin, Erlend Grong, Kazumasa Kuwada, Rob Neel & Anton Thalmaier	Radial processes for sub-Riemannian Brownian motions and applications	Electron. J. Probab. 25 (2020), paper no. 97, 17 pp.
Anton Thalmaier & James Thompson	Exponential integrability and exit times of diffusions on sub-Riemannian and metric measure spaces	Bernoulli 26 (2020), no. 3, 2202-2225
Fabrice Baudoin, Erlend Grong, Kazumasa Kuwada & Anton Thalmaier	Sub-Laplacian comparison theorems on totally geodesic Riemannian foliations	Calc. Var. Partial Differential Equations 58 (2019), no. 4, Art. 130, 38 pp
Anton Thalmaier & James Thompson	Derivative and divergence formulae for diffusion semigroups	Ann. Probab. 47 (2019) no. 2, 743-773
Erlend Grong & Anton Thalmaier	Stochastic completeness and gradient representations for sub-Riemannian manifolds	Potential Anal. 51 (2019), no. 2, 219-254
Li-Juan Cheng, Anton Thalmaier & James Thompson	Functional inequalities on manifolds with non-convex boundary	Sci. China Math. 61 (2018), no. 8, 1421-1436
Li-Juan Cheng, Anton Thalmaier & James Thompson	Quantitative C1-estimates by Bismut formulae	J. Math. Anal. Appl. 465 (2018), no. 2, 803-813
Li-Juan Cheng, Anton Thalmaier & James Thompson	Uniform gradient estimates on manifolds with a boundary and applications	Anal. Math. Phys. 8 (2018), no. 4, 571-588
Li-Juan Cheng & Anton Thalmaier	Evolution systems of measures and semigroups properties on evolving manifolds	Electron. J. Probab. 23 (2018), paper no. 20, 27 pp.
Li-Juan Cheng & Anton Thalmaier	Spectral gap on Riemannian path space over static and evolving manifolds	Journal of Functional Analysis 274 (2018) 959-984
Li-Juan Cheng & Anton Thalmaier	Characterization of pinched Ricci curvature by functional inequalities	Journal of Geometric Analysis 28 (2018), no. 3, 2312-2345
Anton Thalmaier	Geometry of subelliptic diffusions	Geometry, Analysis and Dynamics on sub-Riemannian Manifolds, Vol. II. EMS Series of Lectures in Mathematics, pp. 85-169. European Mathematical Society, Zürich, 2016
Erlend Grong & Anton Thalmaier	Curvature-dimension inequalities on sub-Riemannian manifolds obtained from Riemannian foliations: Part I	Math. Zeitschrift 282 (2016) 99-130
Erlend Grong & Anton Thalmaier	Curvature-dimension inequalities on sub-Riemannian manifolds obtained from Riemannian foliations: Part II	Math. Zeitschrift 282 (2016) 131-164
Hongxin Guo, Robert Philipowski & Anton Thalmaier	On gradient solitons of the Ricci-Harmonic flow	Acta Math. Sin. 31 (2015) 1798-1804
Robert Philipowski & Anton Thalmaier	Heat equation in vector bundles with time-dependent metric	J. Math. Soc. Japan 67 (2015) 1759-1769
Hongxin Guo, Robert Philipowski & Anton Thalmaier	Martingales on manifolds with time-dependent connection	J. Theoret. Probab. 28 (2015) 1038-1062
Hongxin Guo, Robert Philipowski & Anton Thalmaier	An entropy formula for the heat equation on manifolds with time-dependent metric, application to ancient solutions	Potential Analysis 42 (2015) 483-497
Hongxin Guo, Robert Philipowski & Anton Thalmaier	A stochastic approach to the harmonic map heat flow on manifolds with time-dependent Riemannian metric	Stochastic Processes Appl. 124 (2014) 3535-3552
Marc Arnaudon, Anton Thalmaier & Feng-Yu Wang	Equivalent Harnack and gradient inequalities for pointwise curvature lower bound	Bull. Sci. Math. 138 (2014) 643-655
Hongxin Guo, Robert Philipowski & Anton Thalmaier	A note on Chow's entropy functional for the Gauss curvature flow	C. R. Acad. Sci. Paris, Sér. I 351 (2013) 833-835
Hongxin Guo, Robert Philipowski & Anton Thalmaier	Entropy and lowest eigenvalue on evolving manifolds	Pacific J. Math. 264 (2013) 61-82
Marc Arnaudon & Anton Thalmaier	Brownian motion and negative curvature	Random Walks, Boundaries and Spectra, Progress in Probability, Vol. 64, 145-163, Springer Basel, 2011
Anton Thalmaier & Feng-Yu Wang	A stochastic approach to a priori estimates and Liouville theorems for harmonic maps	Bull. Sci. Math. 135 (2011) 816-843
Marc Arnaudon, Koléhè Abdoulaye Coulibaly & Anton Thalmaier	Horizontal diffusion in C¹ path space	Séminaire de Probabilités XLIII, 73-94, Lecture Notes in Mathematics 2006, Springer, 2011
Marc Arnaudon & Anton Thalmaier	The differentiation of hypoelliptic diffusion semigroups	Illinois J. Math. 54 (2010) 1285-1311
Hélène Airault, Paul Malliavin & Anton Thalmaier	Brownian measures on Jordan-Virasoro curves associated to the Weil-Petersson metric	Journal of Functional Analysis 259 (2010) 3037-3079
Marc Arnaudon & Anton Thalmaier	Li-Yau type gradient estimates and Harnack inequalities by stochastic analysis	Advanced Studies in Pure Mathematics 57 (2010) 29-48
Shizan Fang, Dejun Luo & Anton Thalmaier	Stochastic differential equations with coefficients in Sobolev spaces	Journal of Functional Analysis 259 (2010) 1129-1168
Marc Arnaudon, Anton Thalmaier & Feng-Yu Wang	Gradient estimate and Harnack inequality on non-compact Riemannian manifolds	Stochastic Processes Appl. 119 (2009) 3653-3670
Marc Arnaudon, Anton Thalmaier & Stefanie Ulsamer	Existence of non-trivial harmonic functions on Cartan-Hadamard manifolds of unbounded curvature	Math. Zeitschrift 263 (2009) 369-409
Marc Arnaudon, Koléhè Abdoulaye Coulibaly & Anton Thalmaier	Brownian motion with respect to a metric depending on time; definition, existence and applications to Ricci flow	C. R. Acad. Sci. Paris 346 (2008) 773-778
Marc Arnaudon, Bruce K. Driver & Anton Thalmaier	Gradient estimates for positive harmonic functions by stochastic analysis	Stochastic Processes Appl. 117 (2007) 202-220
Marc Arnaudon, Anton Thalmaier & Feng-Yu Wang	Harnack inequality and heat kernel estimates on manifolds with curvature unbounded below	Bull. Sci. Math. 130 (2006) 223-233
Hélène Airault, Paul Malliavin & Anton Thalmaier	Canonical Brownian motion on the space of univalent functions and resolution of Beltrami equations by a continuity method along stochastic flows	J. Math. Pures Appl. 83 (2004) 955-1018
Ana Bela Cruzeiro, Paul Malliavin & Anton Thalmaier	Geometrization of Monte-Carlo numerical analysis of an elliptic operator: strong approximation	C. R. Acad. Sci. Paris 338 (2004) 481-486
Anton Thalmaier & Feng-Yu Wang	Derivative estimates of semigroups and Riesz transforms on vector bundles	Potential Analysis 20 (2004) 105-123
Paul Malliavin & Anton Thalmaier	Numerical error for SDE: Asymptotic expansion and hyperdistributions	C. R. Acad. Sci. Paris 336 (2003) 851-856
Marc Arnaudon, Holger Plank & Anton Thalmaier	A Bismut type formula for the Hessian of heat semigroups	C. R. Acad. Sci. Paris 336 (2003) 661-666
Marc Arnaudon & Anton Thalmaier	Yang-Mills fields and random holonomy along Brownian bridges	Ann. Probab. 31 (2003) 769-790
Emilio Barucci, Paul Malliavin, M.Elvira Mancino, Roberto Renò & Anton Thalmaier	The price-volatility feedback rate: an implementable mathematical indicator of market stability	Mathematical Finance 13 (2003) 17-35
Marc Arnaudon & Anton Thalmaier	Horizontal martingales in vector bundles	Séminaire de Probabilités XXXVI, 419-456, Lecture Notes in Mathematics 1801, Springer, 2003
Hélène Airault, Paul Malliavin & Anton Thalmaier	Support of Virasoro unitarizing measures	C. R. Acad. Sci. Paris 335 (2002) 621-626
Marc Arnaudon, Robert O. Bauer & Anton Thalmaier	A probabilistic approach to the Yang-Mills heat equation	J. Math. Pures Appl. 81 (2002) 143-166
Bruce K. Driver & Anton Thalmaier	Heat equation derivative formulas for vector bundles	Journal of Functional Analysis 183 (2001) 42-108
Marc Arnaudon & Anton Thalmaier	Bismut type differentiation of semigroups	Prob. Theory and Math. Stat. (Vilnius, 1998), 23-32, VSP/TEV, Utrecht and Vilnius, 1999
Marc Arnaudon, Xue-Mei Li & Anton Thalmaier	Manifold-valued martingales, changes of probabilities, and smoothness of finely harmonic maps	Ann. Inst. H. Poincaré Probab. Statist. 35 (1999) 765-792
Anton Thalmaier	Some remarks on the heat flow for functions and forms	Electron. Comm. Probab. 3 (1998) 43-49
Marc Arnaudon & Anton Thalmaier	Complete lifts of connections and stochastic Jacobi fields	J. Math. Pures Appl. 77 (1998) 283-315
Marc Arnaudon & Anton Thalmaier	Stability of stochastic differential equations in manifolds	Séminaire de Probabilités XXXII, 188-214, Lecture Notes in Mathematics 1686, Springer, 1998
Anton Thalmaier & Feng-Yu Wang	Gradient estimates for harmonic functions on regular domains in Riemannian manifolds	Journal of Functional Analysis 155 (1998) 109-124
Anton Thalmaier	On the differentiation of heat semigroups and Poisson integrals	Stochastics and Stochastics Reports 61 (1997) 297-321
Anton Thalmaier	Martingales on Riemannian manifolds and the nonlinear heat equation	Stochastic Analysis and Applications. Proc. of the Fifth Gregynog Symposium. World Scientific Press, 1996, 429-440
Anton Thalmaier	Brownian motion and the formation of singularities in the heat flow for harmonic maps	Probab. Theory Relat. Fields 105 (1996) 335-367

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