Heat equation in vector bundles with time-dependent metric
by Robert Philipowski and Anton Thalmaier

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


The paper is available here:

Robert Philipowski
Anton Thalmaier

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