Pseudo-spherical surfaces of low degree of differentiability

TitlePseudo-spherical surfaces of low degree of differentiability

 

SpeakerJosef Dorfmeister (University of Technology Munich, Germany)

 

Date: 4:00-5:00 pm; September 26; 2013

 

Place: Conference Room A304, Department of Mathematical Sciences

 

Abstract: In differential geometry one usually requires as many degrees of differentiability as is needed for the task at hand.This is somewhat different in the case of pseudo-spherical surfaces, immersions of constant negative Gauss curvature in R^3, since at one hand a theorem of Hilbert, with extensions by Hartman-Wintner and by Efimov,states that the induced metric of such an immersion can never be complete,if the degree of differentiability is at least 2 while on the other hand a theorem of Kuiper states that there exists an isometric C^1- embedding from the Poincare unit disk into R^3. Therefore one asks about which of the usual results of differential geometry still hold for low degrees of differentiability.

       The main interest in this talk will be Minding's Theorem, which states that pseudo-spherical surfaces induce a metric which is locally isometrically isomorphic with the Poincare metric.The talk will start with a theorem by Chern-Hartman-Wintner and will end by a result of Liouville.

 

ContactHui Ma