Li-Yau gradient estimate and entropy formulae for the CR heat equation in a closed pseudohermitian 3-manifold
type: Item
instance of: scholarly article
title: Li-Yau gradient estimate and entropy formulae for the CR heat equation in a closed pseudohermitian 3-manifold
zbMATH Open document ID: 1264.32030
author: Shu-Cheng Chang
author: Ting-Jung Kuo
author: Sin-Hua Lai
published in: Journal of Differential Geometry
publication date: 2012-06-28T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.jdg/1324477409
reviewed by: A. Ghigi
Mathematics Subject Classification ID: 32V20
Mathematics Subject Classification ID: 32W30
Mathematics Subject Classification ID: 58J35
zbMATH DE Number: 6050958
zbMATH Keywords: CR manifold
zbMATH Keywords: pseudohermitian manifold
zbMATH Keywords: Li-Yau estimate
zbMATH Keywords: Perelman entropy formula
MaRDI profile type: Publication
OpenAlex ID: W1494924975
Wikidata QID: Q115170585
DOI: 10.4310/JDG/1324477409
review text: A CR manifold with a fixed contact form is called a pseudohermitian manifold; see [\textit{J. M. Lee}, Am. J. Math. 110, No. 1, 157--178 (1988; Zbl 0638.32019)].NEWLINENEWLINE\textit{H.-D. Cao} and \textit{S.-T. Yau} [Math. Z. 211, No. 3, 485--504 (1992; Zbl 0808.58037)] introduced a CR analogue of the heat flow on a pseudohermitian 3-manifold. In the present paper the authors derive subgradient estimates analogous to the Li-Yau gradient estimate and a Perelman-type entropy formula for this CR heat flow.
description: scientific article; zbMATH DE number 6050958