Heat Equation Derivative Formulas for Vector Bundles
by Bruce K. Driver and Anton Thalmaier

We use martingale methods to give Bismut type derivative formulas for differentials and co-differentials of heat semigroups on forms, and more generally for sections of vector bundles. The formulas are mainly in terms of Weitzenböck curvature terms, in most cases derivatives of the curvature are not involved. In particular, our results improve the formula in Driver (1997) for logarithmic derivatives of the heat kernel measure on a Riemannian manifold. Our formulas also include the formulas in Elworthy and Li (1999).

Journal of Functional Analysis 183 (2001) 42-108 [ORIGINAL ARTICLE]

The paper is available here:

Bruce K. Driver  <driver@euclid.ucsd.edu>
Anton Thalmaier <anton.thalmaier@uni.lu>

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