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ScienceDirect A stochastic approach to the harmonic map heat flow on manifolds with time-dependent Riemannian metric
by
Hongxin Guo
,
Robert Philipowski
,
Anton Thalmaier
BibTeX
@MISC{Guo_sciencedirecta,
author = {Hongxin Guo and Robert Philipowski and Anton Thalmaier},
title = {ScienceDirect A stochastic approach to the harmonic map heat flow on manifolds with time-dependent Riemannian metric},
year = {}
}
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Abstract
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.
