17 citations · 23 across the 3 of their papers we have counts for
7 papers
Harnack Estimates for Conjugate Heat Kernel on Evolving Manifolds
Xiaodong Cao, Hongxin Guo, Hung Tran
In this article we derive Harnack estimates for conjugate heat kernel in an abstract geometric flow. Our calculation involves a correction term D. When D is nonnegative, we are abl…
Harnack Estimates for Nonlinear Heat Equations with Potentials in Geometric Flows
Hongxin Guo, Masashi Ishida
Let be a closed Riemannian manifold with a family of Riemannian metrics evolving by geometric flow , where is a family…
Harnack Estimates for Nonlinear Backward Heat Equations in Geometric Flows
Hongxin Guo, Masashi Ishida
Let be a closed Riemannian manifold with a family of Riemannian metrics evolving by a geometric flow , where is a famil…
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…