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math.DG2006
Limit sets for complete minimal immersions
A. Alarcon, N. Nadirashvili
In this paper we study the behaviour of the limit set of complete proper compact minimal immersions in a regular domain G of R^3. We prove that the second fundamental form of the b…
math.DG2002★ 7 cited
Counterexamples for Local Isometric Embedding
Nikolai Nadirashvili, Yu Yuan
We construct smooth metrics on 2-manifold with nonpositive Gauss curvature which cannot be (C^3) locally isometrically embedded in R^3. Moreover, the Gauss curvature of the metric…