Local Isometric Embedding of Surfaces with Nonpositive Gaussian Curvature
Han, Qing ; Hong, Jia-Xing ; Lin, Chang-Shou
J. Differential Geom., Tome 63 (2003) no. 1, p. 475-520 / Harvested from Project Euclid
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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.
Publié le : 2003-01-14
Classification:  
@article{1090426772,
     author = {Han, Qing and Hong, Jia-Xing and Lin, Chang-Shou},
     title = {Local Isometric Embedding of Surfaces with Nonpositive Gaussian Curvature},
     journal = {J. Differential Geom.},
     volume = {63},
     number = {1},
     year = {2003},
     pages = { 475-520},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1090426772}
}

Han, Qing; Hong, Jia-Xing; Lin, Chang-Shou. Local Isometric Embedding of Surfaces with Nonpositive Gaussian Curvature. J. Differential Geom., Tome 63 (2003) no. 1, pp.  475-520. http://gdmltest.u-ga.fr/item/1090426772/