Date: 27 Mar 2008

Improving Pogorelov’s isometric embedding counterexample

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We construct a C 2,1 metric of non-negative Gauss curvature with no C 2 local isometric embedding in \({\mathbb{R}}^{3}.\)
Dedicate to Professor Wei-Yue Ding on his sixtieth birthday.
Y.Y. was partially supported by an NSF grant, and a Sloan Research Fellowship.