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February 2022 Gradient estimates for the weighted Lichnerowicz equation on smooth metric measure spaces
Liang Zhao, Gang Chen
Rocky Mountain J. Math. 52(1): 335-345 (February 2022). DOI: 10.1216/rmj.2022.52.335

Abstract

We consider the weighted Lichnerowicz equation

fu+cuσ=0

on smooth metric measure spaces, where c0,σ1 are real constants. A local gradient estimate for positive solutions to this equation is derived, and as an application we give a corresponding Harnack inequality.

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Liang Zhao. Gang Chen. "Gradient estimates for the weighted Lichnerowicz equation on smooth metric measure spaces." Rocky Mountain J. Math. 52 (1) 335 - 345, February 2022. https://doi.org/10.1216/rmj.2022.52.335

Information

Received: 4 January 2020; Revised: 6 September 2020; Accepted: 14 September 2020; Published: February 2022
First available in Project Euclid: 19 April 2022

Digital Object Identifier: 10.1216/rmj.2022.52.335

Subjects:
Primary: 58J05
Secondary: 58J35

Keywords: Gradient estimate , Harnack inequality , integral curvature

Rights: Copyright © 2022 Rocky Mountain Mathematics Consortium

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Vol.52 • No. 1 • February 2022
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