Differential Harnack estimates for time-dependent heat equations with potentials in a closed spherical CR 3-manifold
type: Item
instance of: scholarly article
title: Differential Harnack estimates for time-dependent heat equations with potentials in a closed spherical CR 3-manifold
zbMATH Open document ID: 1411.35054
published in: Journal of Mathematical Analysis and Applications
publication date: 2019-02-21T00:00:00Z
review text: In this paper, the author derives differential Harnack estimates for time-dependent heat equations with potentials under the CR Yamabe flow in a closed spherical CR 3-manifold with positive Tanaka-Webster curvature and vanishing torsion. It can be seen as a non-trivial generalization of Li-Yau-Hamilton inequality for the CR Yamabe flow. It is possible that this kind of Harnack estimate could play a central role in the study of the CR Yamabe flow. There are geometric quantities (for example the Tanaka-Webster scalar curvature) which satisfy the equation under the CR Yamabe flow in a closed CR 3-manifold. Indeed, these estimates could be used for understanding the singular models of positive Tanaka-Webster curvature under the CR Yamabe flow. In particular, this estimate should be useful in understanding the Yamabe solitons which one expects to model finite time singularities of the CR Yamabe flow.
reviewed by: Vincenzo Vespri
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 53C44
zbMATH DE Number: 7027386
zbMATH Keywords: CR heat equation
zbMATH Keywords: Li-Yau-Hamilton inequality
zbMATH Keywords: spherical structure
zbMATH Keywords: torsion flow
zbMATH Keywords: CR Yamabe flow
author: Yingbo Han
MaRDI profile type: Publication
full work available at URL: j.jmaa.2018.12.030
OpenAlex ID: W2905421864
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Wikidata QID: Q126210066
DOI: 10.1016/J.JMAA.2018.12.030
description: scientific article; zbMATH DE number 7027386