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

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.


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