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Philipowski, Robert; Thalmaier, Anton

Heat equation in vector bundles with time-dependent metric. (English) Zbl 1429.58042

J. Math. Soc. Japan 67, No. 4, 1759-1769 (2015).
Summary: 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.

Cited in 1 Document

MSC:

58J65 Diffusion processes and stochastic analysis on manifolds
58J35 Heat and other parabolic equation methods for PDEs on manifolds
53E20 Ricci flows

Keywords:

martingale; heat equation; vector bundle; geometric evolution; Ricci flow; Bochner Laplacian
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\textit{R. Philipowski} and \textit{A. Thalmaier}, J. Math. Soc. Japan 67, No. 4, 1759--1769 (2015; Zbl 1429.58042)
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