Gradient Estimates for a Simple Lichnerowicz Equation on Compact Manifolds

XING Jie

doi:10.13371/j.cnki.chin.q.j.m.2015.03.001

Chinese Quarterly Journal of Mathematics >

2015 , Vol. 30 >Issue 3: 317 - 322

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2015.03.001

Gradient Estimates for a Simple Lichnerowicz Equation on Compact Manifolds

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School of Mathematical Sciences, University of Science and Technology of China

XING Jie(1992-) , male, native of Wuhu, Anhui, M.S.D., a lecturer of University of Science and Technology of China, engages in analysis of geometry.

Received date: 2015-03-09

Online published: 2020-11-20

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Abstract

Let（M,g） be a smooth compact Riemannian manifold of dimension n.Denote△f=△-▽f.▽ the weighted Laplacian operator,where f is a smooth real valued function on M.When N is finite and the N-Bakry-Emery Ricci tensor is bounded from below by a constant,we establish local gradient estimates for positive solutions of the following simple Lichnerowicz equation△fu+cu^-α=0 on a compact Riemannian manifold,where α is a positive constant and c is a smooth function.

Key words： gradient estimate; Lichnerowicz equation; weighted Laplacian

Cite this article

XING Jie . Gradient Estimates for a Simple Lichnerowicz Equation on Compact Manifolds[J]. Chinese Quarterly Journal of Mathematics, 2015 , 30(3) : 317 -322 . DOI: 10.13371/j.cnki.chin.q.j.m.2015.03.001

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