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- W1775704635 abstract "We consider two natural problems arising in geometry which are equivalent to the local solvability of specific equations of Monge-Ampere type. These are: the problem of locally prescribed Gaussian curvature for surfaces in R^3, and the local isometric embedding problem for two-dimensional Riemannian manifolds. We prove a general local existence result for a large class of Monge-Ampere equations in the plane, and obtain as corollaries the existence of regular solutions to both problems, in the case that the Gaussian curvature possesses a nondegenerate critical point." @default.
- W1775704635 created "2016-06-24" @default.
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- W1775704635 date "2010-03-11" @default.
- W1775704635 modified "2023-09-27" @default.
- W1775704635 title "Local Solvability of a Class of Degenerate Monge-Ampere Equations and Applications to Geometry" @default.
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