Bounds on the Heat Kernel under the Ricci Flow

Details Bounds on the Heat Kernel under the Ricci Flow Bounds on the Heat Kernel under the Ricci Flow

2010-10-27

arxiv.org/abs/1010.5543v1

Mathematics

Differential Geometry

8 pages

Scientific paper

We establish an estimate for the fundamental solution of the heat equation on a closed Riemannian manifold $M$ of dimension at least 3, evolving under the Ricci flow. The estimate depends on some constants arising from a Sobolev imbedding theorem. Considering the case when the scalar curvature is positive throughout the manifold, at any time, we will obtain, as a corollary, a bound similar to the one known for the fixed metric case.

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