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arXiv · 1310.1868

A stochastic approach to the harmonic map heat flow on manifolds with time-dependent Riemannian metric

Hongxin Guo·Robert Philipowski·Anton Thalmaier
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Abstract

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 Liouville type theorems under appropriate curvature conditions. Space-time harmonic mappings which are defined globally in time correspond to ancient solutions to the harmonic map heat flow. As corollaries, we establish triviality of such ancient solutions in a variety of different situations.

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Hongxin Guo, Robert Philipowski, Anton Thalmaier. 2014-03-26. A stochastic approach to the harmonic map heat flow on manifolds with time-dependent Riemannian metric. https://arxiv.org/abs/1310.1868

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