Geometry Seminar: A. Piubello (Miami)
Geometry Seminar (Geometric Analysis)
Speaker: Anna Piubello (Miami)
Title: Estimates on the Bartnik mass and their geometric implications.
Abstract: In this talk, we will discuss some recent estimates on the Bartnik quasi-local mass for data with nonnegative Gauss curvature and positive mean curvature. This estimate is in terms of the area, the total mean curvature, and a quantity measuring the roundness of the metric. If the ratio between the maximum and the minimum of the Gauss curvature approaches 1, we show that our estimate converges to the sharp bound derived by Miao (2009) for round spheres with positive mean curvature. Furthermore, if the total mean curvature approaches 0, our estimate tends towards the sharp bound found by Mantoulidis and Schoen (2015) for the black hole horizon case. We will then discuss some geometric implications. This is joint work with Pengzi Miao.