BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:General Sobolev metrics on the manifold of all Riemannian metrics 
 - Peter Michor (Universität Wien)
DTSTART:20171113T094500Z
DTEND:20171113T103000Z
UID:TALK94906@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Based on collaborations with M.Bauer\, M.Bruveris\, P.Harms.  
 For a compact manifold $M^m$ equipped with a smooth fixed background Riema
 nnian metric $\\hat g$ we consider the space $\\operatorname{Met}_{H^s(\\h
 at g)}(M)$ of all Riemannian metrics of Sobolev class $H^s$ for real $s>\\
 frac m2$ with respect to $\\hat g$.  The $L^2$-metric on $\\operatorname{M
 et}_{C^\\infty}(M)$ was considered by DeWitt\, Ebin\, Freed and Groisser\,
  Gil-Medrano and Michor\, Clarke. Sobolev metrics of integer order on $\\o
 peratorname{Met}_{C^\\infty}(M)$ were considered in   [M.Bauer\, P.Harms\,
  and P.W. Michor: Sobolev metrics on the manifold of all Riemannian metric
 s. J. Differential Geom.\, 94(2):187-208\, 2013.] In this talk we consider
  variants of these Sobolev metrics which include Sobolev metrics of any po
 sitive  real (not integer) order $s$.  We derive the geodesic equations an
 d show that they are well-posed under some conditions and induce  a locall
 y diffeomorphic geodesic exponential mapping.
LOCATION:Seminar Room 1\, Newton Institute
END:VEVENT
END:VCALENDAR