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Author Khuri, Marcus A
Title The local isometric embedding in R3 of two-dimensional Riemannian manifolds with Gaussian curvature changing sign to finite order on a curve
book jacket
Descript 57 p
Note Source: Dissertation Abstracts International, Volume: 64-04, Section: B, page: 1755
Adviser: Jerry Kazdan
Thesis (Ph.D.)--University of Pennsylvania, 2003
We consider two natural problems arising in geometry which are equivalent to the local solvability of specific equations of Monge-Ampere type. These two problems are: the local isometric embedding problem for two-dimensional Riemannian manifolds, and the problem of locally prescribed Gaussian curvature for surfaces in R3 . 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 vanishes to arbitrary finite order on a single smooth curve
School code: 0175
DDC
Host Item Dissertation Abstracts International 64-04B
Subject Mathematics
0405
Alt Author University of Pennsylvania
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