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.
Citation
Robert PHILIPOWSKI. Anton THALMAIER. "Heat equation in vector bundles with time-dependent metric." J. Math. Soc. Japan 67 (4) 1759 - 1769, October, 2015. https://doi.org/10.2969/jmsj/06741759
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