Heat equation in vector bundles with time-dependent metric
by Robert Philipowski and Anton Thalmaier
Abstract
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.
J. Math. Soc. Japan 67 (2015) 1759-1769
http://dx.doi.org/10.2969/jmsj/06741759
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