A probabilistic representation for heat flow of harmonic map on manifolds with time-dependent Riemannian metric

Xin Chen, Wenjie Ye

Published 2021-01-15Version 1

In this paper we will give a probabilistic representation for the heat flow of harmonic map with time-dependent Riemannian metric via a forward-backward stochastic differential equation on manifolds. Moreover, we can provide an alternative stochastic method for the proof of existence of a unique local solution for heat flow of harmonic map with time-dependent Riemannian metric.