skip to content
 

General Sobolev metrics on the manifold of all Riemannian metrics

Presented by: 
Peter Michor Universität Wien, Universität Wien
Date: 
Monday 13th November 2017 - 09:45 to 10:30
Venue: 
INI Seminar Room 1
Abstract: 
Based on collaborations with M.Bauer, M.Bruveris, P.Harms. For a compact manifold $M^m$ equipped with a smooth fixed background Riemannian metric $\hat g$ we consider the space $\operatorname{Met}_{H^s(\hat g)}(M)$ of all Riemannian metrics of Sobolev class $H^s$ for real $s>\frac m2$ with respect to $\hat g$. The $L^2$-metric on $\operatorname{Met}_{C^\infty}(M)$ was considered by DeWitt, Ebin, Freed and Groisser, Gil-Medrano and Michor, Clarke. Sobolev metrics of integer order on $\operatorname{Met}_{C^\infty}(M)$ were considered in [M.Bauer, P.Harms, and P.W. Michor: Sobolev metrics on the manifold of all Riemannian metrics. J. Differential Geom., 94(2):187-208, 2013.] In this talk we consider variants of these Sobolev metrics which include Sobolev metrics of any positive real (not integer) order $s$. We derive the geodesic equations and show that they are well-posed under some conditions and induce a locally diffeomorphic geodesic exponential mapping.
The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons