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

2021/01/15 by Chen, Xin, Ye, Wenjie
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2101.06024

Abstract

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.

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