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

Hongxin Guo, Robert Philipowski and Anton Thalmaier

Stochastic Processes and their Applications, 2014, vol. 124, issue 11, 3535-3552

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.

Keywords: Harmonic map heat flow; Stochastic analysis on manifolds; Time-dependent geometry (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2014.06.004

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