Local isometric embedding of surfaces with nonpositive Gaussian curvature.

DOI10.4310/jdg/1090426772zbMath1070.53034OpenAlexW1537526697WikidataQ115201107 ScholiaQ115201107MaRDI QIDQ1778004

Qing Han, Chang-Shou Lin, Jia-Xing Hong

Publication date: 26 May 2005

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

Full work available at URL: https://doi.org/10.4310/jdg/1090426772

zbMATH Keywords

Gaussian curvatureGauss-Codazzi equationsNash-Moser-Hörmander iterative scheme

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Surfaces in Euclidean and related spaces (53A05) Degenerate hyperbolic equations (35L80)

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Smooth solutions to a class of mixed type Monge-Ampère equations ⋮ Finite-time degeneration of hyperbolicity without blowup for quasilinear wave equations ⋮ Compactness of Alexandrov‐Nirenberg Surfaces ⋮ 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 ⋮ Hyper-elastic Ricci flow ⋮ Improving Pogorelov's isometric embedding counterexample ⋮ Smooth local solutions to Weingarten equations and \(\sigma_k\)-equations ⋮ Energy estimates for a class of degenerate hyperbolic equations ⋮ Smooth local solutions to degenerate hyperbolic Monge-Ampère equations ⋮ Global BV entropy solutions to the Gauss-Codazzi system ⋮ On the Cauchy problem of degenerate hyperbolic equations ⋮ The semi-global isometric embedding of surfaces with curvature changing signs stably ⋮ Local isometric embedding of surfaces with Gauss curvature changing sign stably across a curve

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