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March, 2003 Local Isometric Embedding of Surfaces with Nonpositive Gaussian Curvature
Qing Han, Jia-Xing Hong, Chang-Shou Lin
J. Differential Geom. 63(3): 475-520 (March, 2003). DOI: 10.4310/jdg/1090426772

Abstract

In this paper, we prove the existence of an isometric embedding near the origin in R3 of a two-dimensional metric with nonpositive Gaussian curvature. The Gaussian curvature can be allowed to be highly degenerate near the origin. Through the Gauss-Codazzi equations, the embedding problem is reduced to a 2 × 2 system of the first order derivaties and is solved via the method of Nash-Moser-Hörmander iterative scheme.

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Qing Han. Jia-Xing Hong. Chang-Shou Lin. "Local Isometric Embedding of Surfaces with Nonpositive Gaussian Curvature." J. Differential Geom. 63 (3) 475 - 520, March, 2003. https://doi.org/10.4310/jdg/1090426772

Information

Published: March, 2003
First available in Project Euclid: 21 July 2004

zbMATH: 1070.53034
MathSciNet: MR2015470
Digital Object Identifier: 10.4310/jdg/1090426772

Rights: Copyright © 2003 Lehigh University

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Vol.63 • No. 3 • March, 2003
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