LI-YAU GRADIENT ESTIMATE AND ENTROPY FORMULAE FOR THE CR HEAT EQUATION IN A CLOSED PSEUDOHERMITIAN 3-MANIFOLD

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/51198

Title:	LI-YAU GRADIENT ESTIMATE AND ENTROPY FORMULAE FOR THE CR HEAT EQUATION IN A CLOSED PSEUDOHERMITIAN 3-MANIFOLD
Authors:	Chang,SC;Kuo,TJ;Lai,SH
Contributors:	數學系
Keywords:	POSITIVE RICCI CURVATURE;VECTOR-FIELDS;MANIFOLDS;SQUARES;SUM;INEQUALITIES;KERNEL;FLOW
Date:	2011
Issue Date:	2012-03-27 18:24:50 (UTC+8)
Publisher:	國立中央大學
Abstract:	In this paper, we derive two subgradient estimates of the CR heat equation in a closed pseudohermitian 3-manifold which are served as the CR version of the Li-Yau gradient estimate. With its applications, we first get a subgradient estimate of the logarithm of the positive solution of the CR heat equation. Secondly, we have the Harnack inequality and upper bound estimate for the heat kernel. Finally, we obtain Perelman-type entropy formulae for the CR heat equation.
Relation:	JOURNAL OF DIFFERENTIAL GEOMETRY
Appears in Collections:	[Department of Mathematics] journal & Dissertation

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