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J. Korean Math. Soc. 2023; 60(5): 1023-1041

Online first article June 13, 2023      Printed September 1, 2023

https://doi.org/10.4134/JKMS.j220589

Copyright © The Korean Mathematical Society.

Li-Yau gradient estimates on closed manifolds under Bakry-\'Emery Ricci curvature conditions

Xing Yu Song, Ling Wu

East China Normal University; East China Normal University

Abstract

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In this paper, motivated by the work of Q.~S.~Zhang in [25], we derive optimal Li-Yau gradient bounds for positive solutions of the $f$-heat equation on closed manifolds with Bakry-\'Emery Ricci curvature bounded below.

Keywords: Li-Yau gradient estimate, Bakry-\'Emery Ricci curvature

MSC numbers: Primary 58J35; Secondary 53C21

Supported by: Research is partially supported by NSFC Grant No. 11971168, Shanghai Science and Technology Innovation Program Basic Research Project STCSM 20JC1412900, and Science and Technology Commission of Shanghai Municipality (STCSM) No. 22DZ2229014.

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