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

by Hongxin Guo, Robert Philipowski and Anton Thalmaier

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.

Stochastic Processes Appl. 124  (2014), 3535-3552  [ORIGINAL ARTICLE]


The paper is available here:

Hongxin Guo
Robert Philipowski
Anton Thalmaier

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