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

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.

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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

Information

Published: October, 2015
First available in Project Euclid: 27 October 2015

zbMATH: 06529334
MathSciNet: MR3417512
Digital Object Identifier: 10.2969/jmsj/06741759

Subjects:
Primary: 58J65
Secondary: 53C44

Rights: Copyright © 2015 Mathematical Society of Japan

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Vol.67 • No. 4 • October, 2015
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