Asian Journal of Mathematics

Volume 21 (2017)

Number 4

A functional inequality on the boundary of static manifolds

Pages: 687 – 696

DOI: https://dx.doi.org/10.4310/AJM.2017.v21.n4.a3

Authors

Kwok-Kun Kwong (Department of Mathematics, National Cheng Kung University, Tainan City, Taiwan)

Pengzi Miao (Department of Mathematics, University of Miami, Coral Gables, Florida, U.S.A.)

Abstract

On the boundary of a compact Riemannian manifold $(\Omega, g)$ whose metric $g$ is static, we establish a functional inequality involving the static potential of $(\Omega, g)$, the second fundamental form and the mean curvature of the boundary $\partial \, \Omega$ respectively.

Keywords

static metrics, functional inequality

2010 Mathematics Subject Classification

53C21, 53C24

Full Text (PDF format)

K.K. Kwong’s research partially supported by Ministry of Science and Technology in Taiwan under grant MOST103-2115-M-006-016-MY3.

P. Miao’s research partially supported by Simons Foundation Collaboration Grant for Mathematicians #281105.

Received 18 June 2015

Published 25 August 2017