## 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.

### MSC:

 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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### References:

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