Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc.

Online first article October 11, 2024

Copyright © The Korean Mathematical Society.

Local gradient estimate on Riemannian manifold with asymptotically non-negative Ricci curvature

Tian Chong, Hui Liu, Lingen Lu, and Jingjing Zhang

Department of Mathematics, Shanghai Polytechnic University, Shanghai 201209 , P.R. China., Institute of Mathematics, Fudan University, Shanghai 200433 , P.R. China.

Abstract

In this paper, we study the asymptotic behavior of the energy densities of harmonic maps, exponentially harmonic functions and positive p-harmonic functions at infinity of a Riemannian manifold with asymptotically non-negative curvature. We prove that the energy densities of bounded harmonic maps, exponentially harmonic functions and positive p-harmonic functions all vanish at infinity.

Keywords: asymptotically non-negative Ricci curvature; exponentially harmonic function; harmonic map; positive p-harmonic function; gradient estimate

MSC numbers: 53B20, 53C21, 53C43, 58E20

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