# Universität AugsburgInstitut für Mathematik

Analysis-Seminar Augsburg-München

University of Pittsburgh

spricht am

Donnerstag, 6. Februar 2020

um

15:00 Uhr

im

Raum 2004 (L1)

über das Thema:

## »On the geometry of flat isometric immersions with Hölder type regularity«

 Abstract: Smooth isometric immersions of flat domains into ٰEuclidean spaces are known to enjoy a rigidity property referred to as developability, provided that the dimension of the target space is not too high. In particular, the images of such isometries from 2d domains into the 3d space are locally ruled surfaces. It has been known since a few years that this rigidity property survives if the second fundamental form of the immersion is merely $L^2$ integrable. On the other hand, convex integration methods à la Nash and Kuiper show that this would no more be the case for $C^{1,\alpha}$ immersions if $\alpha<1/5$. We will show that a geometrically meaningful second fundamental form can be defined for such immersions if $\alpha$ is large enough in order to prove their developability for $\alpha>2/3$.

 Hierzu ergeht herzliche Einladung. Prof. Dr. Bernd Schmidt

[Impressum]      [Datenschutz]      wwwadm@math.uni-augsburg.de,     Mi 15-Jan-2020 08:42:19 MEZ