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Existence results for embedded minimal surfaces of controlled topological type. I. (English) Zbl 0619.49019

The author proves existence results for embedded minimal surfaces of controlled topological type. He uses the approach of Almgren and Simon, to minimize area only among embedded surfaces. Various boundary regularity results for fixed and free boundaries are proved. The results cover situations treated by some other authors where geometric conditions on the boundary configurations were imposed in order to get a surface of given genus. The results of the author also cover the case of minimal surfaces in Riemannian manifolds.
Reviewer: G.Dziuk

MSC:

49Q05 Minimal surfaces and optimization
49Q20 Variational problems in a geometric measure-theoretic setting
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
53C20 Global Riemannian geometry, including pinching
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