Calculus of Variations and Partial Differential Equations

, Volume 32, Issue 3, pp 319-323

First online:

Improving Pogorelov’s isometric embedding counterexample

  • Nikolai NadirashviliAffiliated withLATP, Centre de Mathématiques et Informatique
  • , Yu YuanAffiliated withDepartment of Mathematics, University of Washington Email author 

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