Geometry Seminar: Brian Harvie (NCTS Taiwan)
NB: Held online via Zoom. (Niels Martin Møller's channel - please email him for the URL.)
Speaker: Brian Harvie (NCTS Taiwan)
Title: Equality in the static Minkowski inequality and applications
Abstract: I will discuss the equality case of a Minkowski-type inequality for asymptotically flat static spaces, which are Riemannian manifolds that correspond to static vacuum spacetimes in general relativity. Like the classical Minkowski inequality in R^{n}, the inequality gives a lower bound on the total weighted mean curvature of the manifold boundary and can be proven using inverse mean curvature flow (IMCF). The problem of understanding equality can be reduced to a question about metrics that are called quasi-spherical in the literature.
Our main theorem also gives a uniqueness criteria for Schwarzschild space which we apply to several geometric boundary value problems motivated by physics. In particular, we use our result to extend the classical static black hole uniqueness theorem of Israel to allow for weaker metric decay.