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
The paper is available here:
Back to Homepage