# Hangjun Xu : Inverse Mean Curvature Vector Flows in Spacetimes

One fundamental object in general relativity is the notion of mass. Pointwise energy density and global mass of a spacetime are both well-defined notions of mass. However, the questions of what goes in between the two as the local mass of a given region, and how it relates to the pointwise and global mass are still not well understood. In the case that the spacetime admits a totally geodesic asymptotically flat spacelike slice, the Riemannian Penrose Inequality states that the mass of this slice is lower bounded by the mass of the blackholes. This inequality was proved by Huisken and Ilmanen using inverse mean curvature flow, and by Bray using a different flow. The general Spacetime Penrose Conjecture, which does not assume the existence of such a totally geodesic slice, is still open today. One viable approach is to use the inverse mean curvature vector flow. Such flows do not have a good existence theory. In this talk, we introduce the basic ideas of inverse mean curvature vector flow, and show that there exist many spacetimes in which smooth solutions to such flows exist for all time.

**Category**: Graduate/Faculty Seminar**Duration**: 01:34:52**Date**: April 25, 2014 at 4:25 PM**Views**: 122-
**Tags:**seminar, Graduate/faculty Seminar

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