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December 2009 Maximum Principle and Convergence of Fundamental Solutions for the Ricci Flow
Shu-Yu HSU
Tokyo J. Math. 32(2): 501-516 (December 2009). DOI: 10.3836/tjm/1264170246

Abstract

In this paper we will prove a maximum principle for the solutions of linear parabolic equation on complete non-compact manifolds with a time varying metric. We will prove the convergence of the Neumann Green function of the conjugate heat equation for the Ricci flow in $B_k\times (0,T)$ to the minimal fundamental solution of the conjugate heat equation as $k\to\infty$. We will prove the uniqueness of the fundamental solution under some exponential decay assumption on the fundamental solution. We will also give a detail proof of the convergence of the fundamental solutions of the conjugate heat equation for a sequence of pointed Ricci flow $(M_k\times (-\alpha,0],x_k,g_k)$ to the fundamental solution of the limit manifold as $k\to\infty$ which was used without proof by Perelman in his proof of the pseudolocality theorem for Ricci flow [P].

Citation

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Shu-Yu HSU. "Maximum Principle and Convergence of Fundamental Solutions for the Ricci Flow." Tokyo J. Math. 32 (2) 501 - 516, December 2009. https://doi.org/10.3836/tjm/1264170246

Information

Published: December 2009
First available in Project Euclid: 22 January 2010

zbMATH: 1210.58022
MathSciNet: MR2589959
Digital Object Identifier: 10.3836/tjm/1264170246

Subjects:
Primary: 58J35
Secondary: 53C43

Rights: Copyright © 2009 Publication Committee for the Tokyo Journal of Mathematics

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Vol.32 • No. 2 • December 2009
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