The local isometric embedding in \(\mathbb R^3\) of two-dimensional Riemannian manifolds with Gaussian curvature changing sign to finite order on a curve

DOI10.4310/jdg/1180135679zbMath1130.53017arXiv1003.2244OpenAlexW2963555436WikidataQ115196000 ScholiaQ115196000MaRDI QIDQ2373560

Marcus A. Khuri

Publication date: 12 July 2007

Published in: Journal of Differential Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1003.2244

zbMATH Keywords

isometric embeddingGaussian curvatureMonge-Ampere equationsNash-Moser iteration procedure

Mathematics Subject Classification ID

PDEs of mixed type (35M10) Surfaces in Euclidean and related spaces (53A05) Local submanifolds (53B25) Local Riemannian geometry (53B20)

Related Items (10)

Global Isometric Embedding of Surfaces in $$\mathbb R^3$$ ⋮ Smooth solutions to a class of mixed type Monge-Ampère equations ⋮ On the local isometric embedding in ℝ³of surfaces with zero sets of Gaussian curvature forming cusp domains ⋮ The linearized system for isometric embeddings and its characteristic variety ⋮ Rigidity and flexibility of isometric extensions ⋮ Hyper-elastic Ricci flow ⋮ Boundary value problems for mixed type equations and applications ⋮ Existence of distributional solutions of a closed Dirichlet problem for an elliptic-hyperbolic equation ⋮ C^1,α isometric extensions ⋮ Local isometric embedding of surfaces with Gauss curvature changing sign stably across a curve

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