Reference : Heat equation in vector bundles with time-dependent metric
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/21035
Heat equation in vector bundles with time-dependent metric
English
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 >]
2015
Journal of the Mathematical Society of Japan [=JMSJ]
Mathematical Society of Japan
67
4
1759-1769
Yes (verified by ORBilu)
International
0025-5645
1881-1167
Tokyo
Japan
[en] heat equation on vector bundle ; geometric evolution ; Bochner Laplacian
[en] We derive a stochastic representation formula for solutions of heat-type equations on vector bundles with time-dependent Riemannian metric over manifolds whose Riemannian metric is time-dependent as well. As a corollary we obtain a vanishing theorem for bounded ancient solutions under a curvature condition. Our results apply in particular to the case of differential forms.
Researchers
http://hdl.handle.net/10993/21035
10.2969/jmsj/06741759
http://projecteuclid.org/euclid.jmsj/1445951165
FnR ; FNR7628746 > Anton Thalmaier > GEOMREV > Geometry of random evolutions > 01/03/2015 > 28/02/2018 > 2014

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