Constant mean curvature surfaces in a half-space of $\mathbf{R}^3$ with boundary in the boundary of the half-space

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Constant Mean Curvature Surfaces in a Half-Space of R With Boundary in the Boundary of the Half-Space

The structure of the set of compact constant mean curvature surfaces whose boundary is a given Jordan curve in R seems far from being understood. We shall consider a simple, but interesting, situation concerning this problem: Assume that M be an embedded compact H-surface in R+ = {x3 ≥ 0} with ∂M = Γ ⊂ P = {x3 = 0}. Then, there is little known about the geometry and topology of M in terms of Γ....

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ژورنال

عنوان ژورنال: Journal of Differential Geometry

سال: 1996

ISSN: 0022-040X

DOI: 10.4310/jdg/1214459410