Universität Augsburg
Institut für Mathematik

Siegel der Universität Augsburg

 

Oberseminar Differentialgeometrie

 

Professor Dr. Bernhard Hanke
Universität Augsburg

 
spricht am
 
Montag, 30. Mai 2022
 
um
 
16 Uhr s.t.
 
im
 
Raum L1/2004 bzw. ZOOM (hybride Veranstaltung)
 
über das Thema:
 

»Lipschitz rigidity for scalar curvature «

Abstract:

Lower scalar curvature bounds on spin Riemannian manifolds exhibit remarkable rigidity properties determined by the index theory of Dirac operators. A fundamental result of Llarull states that there is no smooth Riemannian metric on the n-sphere which dominates the round metric and whose scalar curvature is greater than or equal to the scalar curvature of the round metric, except the round metric itself. A similar result holds for smooth comparison maps from spin Riemannian manifolds to round spheres.

In a joint work with Simone Cecchini and Thomas Schick, we discuss these results for Riemannian metrics with regularity smaller than C^1 and Lipschitz comparison maps. This uses spectral properties of Dirac operators twisted with Lipschitz bundles and the theory of quasi-regular maps.


 

Hierzu ergeht herzliche Einladung.
Prof. Dr. Wolfgang Steimle
 

Kaffee, Tee und Gebäck eine halbe Stunde vor Vortragsbeginn im Raum 2006 (L1).



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