Bounds on the heat kernel under the Ricci flow

Băileşteanu, Mihai

doi:10.1090/S0002-9939-2011-11057-8

Bounds on the heat kernel under the Ricci flow

Author: Mihai Băileşteanu
Journal: Proc. Amer. Math. Soc. 140 (2012), 691-700
MSC (2010): Primary 53C44, 35K05, 35K08; Secondary 53B20, 53B21
DOI: https://doi.org/10.1090/S0002-9939-2011-11057-8
Published electronically: June 9, 2011
MathSciNet review: 2846338
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Abstract: We establish an estimate for the fundamental solution of the heat equation on a closed Riemannian manifold of dimension at least , 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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