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1-16/17吴文俊数学重点实验室微分方程方向系列报告【邱国寰】
报告题目: Introduction to h-principle for isometric embeddings in R^3 报告人:邱国寰 (加拿大McGill大学) 地点:管理科研楼 时 间 1月16日 14:00-16:30 1月17日 14:00-16:30 教 室 1418教室 1518教室 Characterize those intrinsic metrics on a surface which can be realized as embeddings into three space is an important well-known question.
The famous result of Nash (the paper in 1954)-Kuiper says that any short embedding in codimension one can be uniformly approximated by C^1
isometric embeddings. On the other hand there is rigidity theorem for C^2 isometric embedding.Borisov extended the rigidity result to embeddings
of class C^1,a with a>2/3 and announced the non-rigidity theorem to local C^1,a embeddings with a<1/7. And this exponent was extend by Conti,
De Lellis, Inauen and Szekelyhidi to 1/5 so far. But the best holder exponent for this h-principle phenomenon is still open. In these seminars,
we will introduce this problem and the Nash's technique for this problem. The main references are: 1. Nash,J C^1 isometric imbeddings. Ann.Math (1954). 2. Sergio Conti, Camillo De Lellis, and Laszlo Szekelyhidi Jr, H-Principle and Rigidity for C^1,a isometric embeddings.

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