# Heat flow on Finsler manifolds

@article{Ohta2008HeatFO,
title={Heat flow on Finsler manifolds},
author={Shin-Ichi Ohta and Karl-Theodor Sturm},
journal={Communications on Pure and Applied Mathematics},
year={2008},
volume={62}
}
• Published 8 August 2008
• Mathematics
• Communications on Pure and Applied Mathematics
This paper studies the heat flow on Finsler manifolds. A Finsler manifold is a smooth manifold M equipped with a Minkowski norm F(x, ·) : TxM → ℝ+ on each tangent space. Mostly, we will require that this norm be strongly convex and smooth and that it depend smoothly on the base point x. The particular case of a Hilbert norm on each tangent space leads to the important subclasses of Riemannian manifolds where the heat flow is widely studied and well understood. We present two approaches to the…
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