Local Solvability of a Class of Degenerate Monge-Ampere Equations and Applications to Geometry - Mathematics > Analysis of PDEsReport as inadecuate




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Abstract: We consider two natural problems arising in geometry which are equivalent tothe local solvability of specific equations of Monge-Ampere type. These are:the problem of locally prescribed Gaussian curvature for surfaces in R^3, andthe local isometric embedding problem for two-dimensional Riemannian manifolds.We prove a general local existence result for a large class of Monge-Ampereequations in the plane, and obtain as corollaries the existence of regularsolutions to both problems, in the case that the Gaussian curvature possesses anondegenerate critical point.



Author: Marcus A. Khuri

Source: https://arxiv.org/







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