Improving Pogorelov's isometric embedding counterexample

DOI10.1007/S00526-007-0140-7zbMath1147.53017OpenAlexW1973625050WikidataQ125028228 ScholiaQ125028228MaRDI QIDQ927295

Yu Yuan, Nikolai S. Nadirashvili

Publication date: 4 June 2008

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-007-0140-7

zbMATH Keywords

Gauss curvaturePogerolov's metric

Mathematics Subject Classification ID

Surfaces in Euclidean and related spaces (53A05) Local submanifolds (53B25)

Related Items (3)

Isometric embeddings in imaging and vision: facts and fiction ⋮ On the local isometric embedding in ℝ³of surfaces with zero sets of Gaussian curvature forming cusp domains ⋮ Geometric, algebraic, and analytic descendants of Nash isometric embedding theorems

Cites Work

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• The local isometric embedding in \(R^ 3\) of 2-dimensional Riemannian manifolds with nonnegative curvature
• Local isometric embedding of surfaces with nonpositive Gaussian curvature.
• The local isometric embedding inR3 of two-dimensional riemannian manifolds with gaussian curvature changing sign cleanly
• On the isometric embedding of surfaces with Gauss curvature changing sign cleanly
• Local Smooth Isometric Embeddings of Low Dimensional Riemannian Manifolds into Euclidean Spaces

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