Asian Journal of Mathematics
Volume 21 (2017)
A functional inequality on the boundary of static manifolds
Pages: 687 – 696
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
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