Journal of the Mathematical Society of Japan

Heat equation in vector bundles with time-dependent metric


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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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J. Math. Soc. Japan, Volume 67, Number 4 (2015), 1759-1769.

First available in Project Euclid: 27 October 2015

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Primary: 58J65: Diffusion processes and stochastic analysis on manifolds [See also 35R60, 60H10, 60J60]
Secondary: 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.)

Martingale heat equation vector bundle geometric evolution Ricci flow Bochner Laplacian


PHILIPOWSKI, Robert; THALMAIER, Anton. Heat equation in vector bundles with time-dependent metric. J. Math. Soc. Japan 67 (2015), no. 4, 1759--1769. doi:10.2969/jmsj/06741759.

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