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

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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Year of publication:	2014
Authors:	Guo, Hongxin ; Philipowski, Robert ; Thalmaier, Anton
Published in:	Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 124.2014, 11, p. 3535-3552
Publisher:	Elsevier
Subject:	Harmonic map heat flow \| Stochastic analysis on manifolds \| Time-dependent geometry

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10010907046