The plateau problem in Alexandrov spaces
نویسندگان
چکیده
منابع مشابه
A Problem of Alexandrov
0 Introduction For n 2, Let M n be a nite convex, not necessarily smooth, hypersur-face in Euclidean space R n+1 containing the origin. More precisely, M n is the boundary of some convex domain in R n+1 containing a neighborhood of the origin. We write M n = fR(x) = (x)x j x 2 S n g, where is a function from S n to R +. Let : M n ! S n denote the generalized Gauss map, namely, (Y) is the set of...
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1. A comparison theorem for complete Riemannian manifolds with sectional curvatures ≥ k says that distance functions in such manifolds are more concave than in the model space Sk of constant curvature k. In other words, the restriction of any distance function distp to any geodesic γ (always parametrised by the arclength) satisfies a certain concavity condition (∗)k. For example, the condition ...
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ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 2010
ISSN: 0022-040X
DOI: 10.4310/jdg/1287580967