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

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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.

Original language	English
Pages (from-to)	223-256
Number of pages	34
Journal	Asian Journal of Mathematics
Volume	22
Issue number	2
DOIs	https://doi.org/10.4310/AJM.2018.v22.n2.a2
Publication status	Published - 2018

Keywords

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

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.4310/AJM.2018.v22.n2.a2

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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 of Boston, 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

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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

Abstract

Keywords

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