Martingales on Riemannian manifolds and the nonlinear heat equation
by Anton Thalmaier

Solutions to the nonlinear heat equation for maps between Riemannian manifolds are studied by determining starting points for martingales on Riemannian manifolds with prescribed terminal values. Monotonicity properties of the Riemannian quadratic variation for these martingales allow to explain blow-up of the heat flow in finite time. Moreover, the probabilistic construction of martingales with given terminal state is discussed, and partial regularity results for the heat flow are established.

In: I.M. Davies, A. Truman and K.D. Elworthy (Eds.)
Stochastic Analysis and Applications.
Proc. of the Fifth Gregynog Symposium, Gregynog, 1995.
Singapore: World Scientific Press, 1996, 429-440.

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Anton Thalmaier <>

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