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Schoen's Conjecture for Limits of Isoperimetric Surfaces

Offered By: Erwin Schrödinger International Institute for Mathematics and Physics (ESI) via YouTube

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Differential Geometry Courses Euclidean Spaces Courses Scalar Curvature Courses Riemannian Manifolds Courses

Course Description

Overview

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Explore a mathematical lecture from the Workshop on "Mathematical Relativity: Past, Present, Future" held at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into Thomas Körber's presentation on Schoen's conjecture for limits of isoperimetric surfaces, which addresses a fundamental question in Riemannian geometry. Learn about the recent work by Körber and Eichmair confirming Schoen's conjecture for asymptotically flat Riemannian manifolds of dimensions 3 to 7, where the area-minimizing hypersurface is the limit of large isoperimetric hypersurfaces. Discover their contrasting findings in spatial Schwarzschild geometries, where non-compact area-minimizing hypersurfaces form a foliation. Gain insights into the interplay between scalar curvature, area-minimizing hypersurfaces, and the geometry of asymptotically flat manifolds in this 57-minute talk that advances our understanding of mathematical relativity.

Syllabus

Thomas Körber - Schoen's conjecture for limits of isoperimetric surfaces


Taught by

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

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