Reference : A stochastic approach to the harmonic map heat flow on manifolds with time-dependent ...
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/13908
A stochastic approach to the harmonic map heat flow on manifolds with time-dependent Riemannian metric
English
Guo, Hongxin [Wenzhou University > School of Mathematics and Information Science]
Philipowski, Robert mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Thalmaier, Anton mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Nov-2014
Stochastic Processes and their Applications
Elsevier
124
11
3535-3552
Yes (verified by ORBilu)
International
0304-4149
[en] 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.
Researchers ; Professionals
http://hdl.handle.net/10993/13908
10.1016/j.spa.2014.06.004
http://www.sciencedirect.com/science/article/pii/S0304414914001343

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