数学科学系

Department of Mathematical Sciences

Pseudo-spherical surfaces of low degree of differentiability

报告题目: Pseudo-spherical surfaces of low degree of differentiability

 

报告人: Josef Dorfmeister (University of Technology Munich, Germany)

 

时间: 2013926 (周四) 16:00-17:00

 

地点: 理科楼数学系A304

 

摘要: 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.

报告人简介:Josef Dorfmeister教授,著名微分几何学家,在齐性kaehler流形,球面中等参超曲面的分类问题上作出过重要的贡献。近年来,与Franz Pedit, Hongyou Wuloop群创立DPW方法,是构造到对称空间的调和曲面,特别是三维欧式空间中非紧常平均曲率曲面的有效的方法,被广泛应用到相关几何构造问题中。

 

联系人:马辉