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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…
math.AP2002
Linearity of homogeneous order one solutions to elliptic equations in dimension three
Qing Han, Nikolai Nadirashvili, Yu Yuan
We prove that any homogeneous order one solution to 3-d nondivergence elliptic equations must be linear.