On the stability of higher dimensions

General Relativity, Geometry and Analysis: beyond the first 100 years after Einstein

26 November 11:00 - 12:00

Pieter Blue - University of Edinburgh

There is a large class of Kaluza-Klein type spaces given by the Cartesian product of 1+n dimensional Minkowski space with a Ricci-flat Riemannian manifold, called the internal space. These are solutions of the Einstein equation. This talk will show that these spaces are stable as solutions of the Einstein equation when n is sufficiently large and, at least, when the internal space is a torus. This requires taking the intersection of methods for quasilinear wave and Klein-Gordon equations. This stability result is a related to a conjecture of Penrose concerning the validity of string theory.
Lars Andersson
Max Planck Institute for Gravitational Physics (Albert Einstein Institute)
Mattias Dahl
KTH Royal Institute of Technology
Philippe G. LeFloch
Sorbonne University
Richard Schoen
University of California, Irvine


Mattias Dahl


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