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

Xin Chen; Wenjie Ye

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arXiv · 2101.06024

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

Xin Chen·Wenjie Ye

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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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BibTeX RIS

Xin Chen, Wenjie Ye. 2021-01-15. A probabilistic representation for heat flow of harmonic map on manifolds with time-dependent Riemannian metric. https://arxiv.org/abs/2101.06024

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