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12:00 pm Monday, March 21, 2011 Stulken Geometry-Analysis Seminar: Isoperimetric Structure of Initial Data Sets.by
Michael Eichmair (MIT) in HB 427- I will present recent joint work with Jan Metzger. A basic question in mathematical relativity is how geometric properties of an asymptotically flat manifold (or initial data set) encode information about the physical properties of the space time that it is embedded in. For example, the square root of the area of the outermost minimal surface of an initial data with non-negative scalar curvature provides a lower bound for the "mass" of its associated space time, as was conjectured by Penrose and proven by Bray and Huisken-Ilmanen. Other special surfaces that have been studied in this context include stable constant mean curvature surfaces or isoperimetric surfaces. I will explain why positive mass works to the effect that large stable constant mean curvature surfaces are always isoperimetric. This answers a question of Bray's and complements the results by Huisken-Yau and Qing-Tian on the "global uniqueness problem for stable CMC surfaces" in initial data sets with positive scalar curvature.
Submitted by lr7@rice.edu |