An upper bound of the heat kernel along the harmonic-Ricci flow

Shouwen Fang; Tao Zheng

doi:10.1007/s00229-016-0825-3

An upper bound of the heat kernel along the harmonic-Ricci flow

Shouwen Fang, Tao Zheng^*

^*Corresponding author for this work

School of Mathematics and Statistics

Yangzhou University

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

4 Citations (Scopus)

Abstract

In this paper, we first derive a Sobolev inequality along the harmonic-Ricci flow. We then prove a linear parabolic estimate based on the Sobolev inequality and Moser’s iteration. As an application, we will obtain an upper bound estimate for the heat kernel under the flow.

Original language	English
Pages (from-to)	1-18
Number of pages	18
Journal	Manuscripta Mathematica
Volume	151
Issue number	1-2
DOIs	https://doi.org/10.1007/s00229-016-0825-3
Publication status	Published - 1 Sept 2016

Keywords

53C21
53C44

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10.1007/s00229-016-0825-3

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Fang, S., & Zheng, T. (2016). An upper bound of the heat kernel along the harmonic-Ricci flow. Manuscripta Mathematica, 151(1-2), 1-18. https://doi.org/10.1007/s00229-016-0825-3

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AB - In this paper, we first derive a Sobolev inequality along the harmonic-Ricci flow. We then prove a linear parabolic estimate based on the Sobolev inequality and Moser’s iteration. As an application, we will obtain an upper bound estimate for the heat kernel under the flow.

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An upper bound of the heat kernel along the harmonic-Ricci flow

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Keywords

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