报告题目： Introduction to h-principle for isometric embeddings in R^3
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.