6 papers
A stochastic approach to the harmonic map heat flow on manifolds with time-dependent Riemannian metric
Hongxin Guo, Robert Philipowski, Anton Thalmaier
We first prove stochastic representation formulae for space-time harmonic mappings defined on manifolds with evolving Riemannian metric. We then apply these formulae to derive Liou…
An entropy formula for the heat equation on manifolds with time-dependent metric, application to ancient solutions
Hongxin Guo, Robert Philipowski, Anton Thalmaier
We introduce a new entropy functional for nonnegative solutions of the heat equation on a manifold with time-dependent Riemannian metric. Under certain integral assumptions, we sho…
Martingales on manifolds with time-dependent connection
Hongxin Guo, Robert Philipowski, Anton Thalmaier
We define martingales on manifolds with time-dependent connection, extending in this way the theory of stochastic processes on manifolds with time-changing geometry initiated by Ar…
Entropy and lowest eigenvalue on evolving manifolds
Hongxin Guo, Robert Philipowski, Anton Thalmaier
In this note we determine the first two derivatives of the classical Boltzmann-Shannon entropy of the conjugate heat equation on general evolving manifolds. Based on the second der…
Coupling of Brownian motions and Perelman's L-functional
Kazumasa Kuwada, Robert Philipowski
We show that on a manifold whose Riemannian metric evolves under backwards Ricci flow two Brownian motions can be coupled in such a way that the expectation of their normalized L-d…
Non-explosion of diffusion processes on manifolds with time-dependent metric
Kazumasa Kuwada, Robert Philipowski
We study the problem of non-explosion of diffusion processes on a manifold with time-dependent Riemannian metric. In particular we obtain that Brownian motion cannot explode in fin…