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Improving Pogorelov’s isometric embedding counterexample

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Abstract

We construct a C 2,1 metric of non-negative Gauss curvature with no C 2 local isometric embedding in \({\mathbb{R}}^{3}.\)

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Authors and Affiliations

  1. LATP, Centre de Mathématiques et Informatique, 39, rue F. Joliot-Curie, 13453, Marseille Cedex, France

    Nikolai Nadirashvili

  2. Department of Mathematics, University of Washington, Box 354350, Seattle, WA, 98195, USA

    Yu Yuan

Authors
  1. Nikolai Nadirashvili
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  2. Yu Yuan
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Corresponding author

Correspondence to Yu Yuan.

Additional information

Dedicate to Professor Wei-Yue Ding on his sixtieth birthday.

Y.Y. was partially supported by an NSF grant, and a Sloan Research Fellowship.

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Nadirashvili, N., Yuan, Y. Improving Pogorelov’s isometric embedding counterexample. Calc. Var. 32, 319–323 (2008). https://doi.org/10.1007/s00526-007-0140-7

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  • DOI: https://doi.org/10.1007/s00526-007-0140-7

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