Hamilton's gradient estimate for the heat kernel on complete manifolds

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

In this paper we extend a gradient estimate of R. Hamilton for positive solutions to the heat equation on closed manifolds to bounded positive solutions on complete, non-compact manifolds with Rc ≥-Kg. We accomplish this extension via a maximum principle of L. Karp and P. Li and a Berstein-type estimate on the gradient of the solution. An application of our result, together with the bounds of P. Li and S.T. Yau, yields an estimate on the gradient of the heat kernel for complete manifolds with non-negative Ricci curvature that is sharp in the order of t for the heat kernel on ℝn.

Original languageEnglish (US)
Pages (from-to)3013-3019
Number of pages7
JournalProceedings of the American Mathematical Society
Volume135
Issue number9
DOIs
StatePublished - Sep 2007
Externally publishedYes

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Gradient Estimate
Heat Kernel
Positive Solution
Gradient
Noncompact Manifold
Nonnegative Curvature
Ricci Curvature
Maximum Principle
Heat Equation
Estimate
Maximum principle
Closed
Hot Temperature

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Hamilton's gradient estimate for the heat kernel on complete manifolds. / Kotschwar, Brett.

In: Proceedings of the American Mathematical Society, Vol. 135, No. 9, 09.2007, p. 3013-3019.

Research output: Contribution to journalArticle

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