## 2008 DG-MP-PDE Seminar-10

• Date: 04/29/2008
Lecturer(s):
Pengzi Miao (Monash University)
Location:

University of British Columbia

Topic:

On the size of the outermost minimal surface in a compact 3-manifold with a spherical boundary

Description:

Let $M$ be a compact three dimensional Riemannian manifold with a
non-empty boundary. Suppose $S$ is a boundary component of $M$ such
that its mean curvature vector\uffff points inward. Assume $S_H$ is a
closed minimal surface in $M$ which has the properties that $S_H$
and $S$ bounds a region $\Omega$ in $M$ and there is no other
closed minimal surfaces in $\Omega$. Assuming that $M$ has
nonnegative scalar curvature, we are interested in estimating the area
of $S_H$ from above by the geometry data of $S$. A result of this
type could be viewed as a localized statement of the Riemannian Penrose
Inequality in general relativity. In this talk, we derive such an
inequality under the additional assumption that $S$ is metrically a
round sphere.

Schedule:

3:30pm, WMAX 110