Improving Pogorelov’s isometric embedding counterexample

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

Abstract

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.