Asian Journal of Mathematics

Volume 21 (2017)

Number 4

A functional inequality on the boundary of static manifolds

Pages: 687 – 696



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.)


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.


static metrics, functional inequality

2010 Mathematics Subject Classification

53C21, 53C24

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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.

Paper received on 18 June 2015.