Siegel der Universität Augsburg

Universität Augsburg
Institut für Mathematik

Siegel der Universität Augsburg

 

Analysis-Seminar Augsburg-München

 

Dr. Mario Santilli
Max-Planck-Institut, Potsdam

 
spricht am
 
Donnerstag, 26. Oktober 2017
 
um
 
16:30 Uhr
 
im
 
Raum 2004 (L1)
 
über das Thema:
 

»A notion of curvature for closed subsets of Euclidean space with applications to generalized minimal submanifolds of arbitrary codimension«

Abstract:
Abstract: A second fundamental form is introduced for arbitrary closed subsets of Euclidean space, extending the same notion introduced by J. Fu for sets of positive reach. We extend well known integral-geometric formulas to this general setting and we provide a structural result in terms of second fundamental forms of submanifolds of class 2 that is new even for sets of positive reach. For a large class of minimal submanifolds, which include viscosity solutions of the minimal surface system and rectifiable stationary varifolds of arbitrary codimension and higher multiplicities, we prove the area formula for the generalized Gauss map in terms of the discriminant of the second fundamental form and, adapting techniques from the theory of viscosity solutions of elliptic equations to our geometric setting, we conclude a natural second-order-differentiability property almost everywhere.

 

Hierzu ergeht herzliche Einladung.
Prof. Dr. Bernd Schmidt
 

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



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