Compactness for immersions of prescribed Gaussian curvature II - geometric aspects

Details Compactness for immersions of prescribed Gaussian curvature II - geometric aspects Compactness for immersions of prescribed Gaussian curvature II - geometric aspects

2010-02-16

arxiv.org/abs/1002.2982v3

Mathematics

Differential Geometry

Formerly "The Plateau Problem in Hadamard Manifolds". Minor changes improving readability and reflecting subsequent developmen

Scientific paper

We develop a compactness result near the boundary for families of locally
convex immersions. We also develop a mod 2 degree theory for immersion of
constant (and prescribed) Gaussian curvature with prescribed boundary. These
are then used to solve the Plateau problem for immersions of constant (and
prescribed) Gaussian curvature in general Hadamard manifolds.

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