Cr Li-Yau gradient estimate for witten Laplacian via Bakry-Emery Pseudohermitian Ricci Curvature

Der Chen Chang; Shu Cheng Chang; Ting Jung Kuo; Sin Hua Lai

doi:10.4310/AJM.2018.v22.n2.a2

Cr Li-Yau gradient estimate for witten Laplacian via Bakry-Emery Pseudohermitian Ricci Curvature

Der Chen Chang
, Shu Cheng Chang
, Ting Jung Kuo
, Sin Hua Lai

數學系

研究成果: 雜誌貢獻 › 期刊論文 › 同行評審

1 引文斯高帕斯（Scopus）

摘要

In this paper, we derive the sub-gradient estimate of the CR heat equation associated with the Witten sub-Laplacian via the Bakry-Emery Pseudohermitian Ricci Curvature. With its applications, we first get a Harnack inequality for the positive solution of this CR heat equation in a closed pseudohermitian (2n + 1)-manifold. Secondly, we obtain Perelman-type linear entropy formulae for this CR heat equation.

原文	英語
頁（從 - 到）	223-256
頁數	34
期刊	Asian Journal of Mathematics
卷	22
發行號	2
DOIs	https://doi.org/10.4310/AJM.2018.v22.n2.a2
出版狀態	已發佈 - 2018

ASJC Scopus subject areas

一般數學
應用數學

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10.4310/AJM.2018.v22.n2.a2

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@article{d3c6c404392c4c5e865fd728ed254583,

title = "Cr Li-Yau gradient estimate for witten Laplacian via Bakry-Emery Pseudohermitian Ricci Curvature",

abstract = "In this paper, we derive the sub-gradient estimate of the CR heat equation associated with the Witten sub-Laplacian via the Bakry-Emery Pseudohermitian Ricci Curvature. With its applications, we first get a Harnack inequality for the positive solution of this CR heat equation in a closed pseudohermitian (2n + 1)-manifold. Secondly, we obtain Perelman-type linear entropy formulae for this CR heat equation.",

keywords = "Bakry-Emery Pseudohermitian Ricci Curvature, CR heat equation, Harnack inequality, Li-Yau gradient estimate, Perelman Entropy formulae, Pseudohermitian manifold, Witten Laplacian",

author = "Chang, \{Der Chen\} and Chang, \{Shu Cheng\} and Kuo, \{Ting Jung\} and Lai, \{Sin Hua\}",

note = "Publisher Copyright: {\textcopyright} 2018 International Press.",

year = "2018",

doi = "10.4310/AJM.2018.v22.n2.a2",

language = "English",

volume = "22",

pages = "223--256",

journal = "Asian Journal of Mathematics",

issn = "1093-6106",

publisher = "International Press, Inc.",

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TY - JOUR

T1 - Cr Li-Yau gradient estimate for witten Laplacian via Bakry-Emery Pseudohermitian Ricci Curvature

AU - Chang, Der Chen

AU - Chang, Shu Cheng

AU - Kuo, Ting Jung

AU - Lai, Sin Hua

PY - 2018

Y1 - 2018

N2 - In this paper, we derive the sub-gradient estimate of the CR heat equation associated with the Witten sub-Laplacian via the Bakry-Emery Pseudohermitian Ricci Curvature. With its applications, we first get a Harnack inequality for the positive solution of this CR heat equation in a closed pseudohermitian (2n + 1)-manifold. Secondly, we obtain Perelman-type linear entropy formulae for this CR heat equation.

AB - In this paper, we derive the sub-gradient estimate of the CR heat equation associated with the Witten sub-Laplacian via the Bakry-Emery Pseudohermitian Ricci Curvature. With its applications, we first get a Harnack inequality for the positive solution of this CR heat equation in a closed pseudohermitian (2n + 1)-manifold. Secondly, we obtain Perelman-type linear entropy formulae for this CR heat equation.

KW - Bakry-Emery Pseudohermitian Ricci Curvature

KW - CR heat equation

KW - Harnack inequality

KW - Li-Yau gradient estimate

KW - Perelman Entropy formulae

KW - Pseudohermitian manifold

KW - Witten Laplacian

UR - https://www.scopus.com/pages/publications/85048625131

UR - https://www.scopus.com/pages/publications/85048625131#tab=citedBy

U2 - 10.4310/AJM.2018.v22.n2.a2

DO - 10.4310/AJM.2018.v22.n2.a2

M3 - Article

AN - SCOPUS:85048625131

SN - 1093-6106

VL - 22

SP - 223

EP - 256

JO - Asian Journal of Mathematics

JF - Asian Journal of Mathematics

IS - 2

ER -

Cr Li-Yau gradient estimate for witten Laplacian via Bakry-Emery Pseudohermitian Ricci Curvature

摘要

ASJC Scopus subject areas

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