Journal of the Mathematical Society of Japan

Heat equation in vector bundles with time-dependent metric

Robert PHILIPOWSKI and Anton THALMAIER

Full-text: Open access

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.

Article information

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

Dates
First available in Project Euclid: 27 October 2015

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1445951165

Digital Object Identifier
doi:10.2969/jmsj/06741759

Mathematical Reviews number (MathSciNet)
MR3417512

Zentralblatt MATH identifier
06529334

Subjects
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.)

Keywords
Martingale heat equation vector bundle geometric evolution Ricci flow Bochner Laplacian

Citation

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. https://projecteuclid.org/euclid.jmsj/1445951165


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