Uniqueness of large area-constrained Willmore spheres in initial data sets

Abstract: The Hawking mass of an area-constrained Willmore sphere is a useful quasi-local measure for the strength of the gravitational field of an initial data set for the Einstein field equations. If the scalar curvature satisfies certain asymptotic assumptions, the asymptotic region of such an initial data set is foliated by large area-constrained Willmore spheres with non-negative Hawking mass. It has been conjectured that these are the only such spheres. In this talk, I will present a proof of this conjecture for all large area-constrained Willmore spheres with non-negative Hawking mass and outer radius less than the logarithm of the inner radius. This is joint work with Michael Eichmair, Jan Metzger, and Felix Schulze.

general relativity and quantum cosmologymathematical physicsanalysis of PDEsdifferential geometry

Audience: researchers in the topic

( video )

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JoMaReC - Joint Online Mathematical Relativity Colloquium

Series comments: This monthly online colloquium is meant to be accessible to and informative for mathematicians and mathematical physicists with a background in General Relativity, widely interpreted to include Lorentzian Geometry, and Geometric Analysis of various Partial Differential Equations related to General Relativity.

It is aimed to present motivation and applications of particular results and/or introduce specific subfields, while refraining from too much technicalities.

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