The moduli space of complete embedded constant mean curvature surfaces
نویسندگان
چکیده
منابع مشابه
The Moduli Space of Complete Embedded Constant Mean Curvature Surfaces
We examine the space of surfaces in R which are complete, properly embedded and have nonzero constant mean curvature. These surfaces are noncompact provided we exclude the case of the round sphere. We prove that the space Mk of all such surfaces with k ends (where surfaces are identified if they differ by an isometry of R) is locally a real analytic variety. When the linearization of the quasil...
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In this paper we refine the construction and related estimates for complete Constant Mean Curvature surfaces in Euclidean three-space developed in [12] by adopting the more precise and powerful version of the methodology which was developed in [16]. As a consequence we remove the severe restrictions in establishing embeddedness for complete Constant Mean Curvature surfaces in [12] and we produc...
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In this paper we prove a maximum principle at infinity for properly embedded surfaces with constant mean curvature H > 0 in the 3-dimensional Euclidean space. We show that no one of these surfaces can lie in the mean convex side of another properly embedded H surface. We also prove that, under natural assumptions, if the surface lies in the slab |x3| < 1/2H and is symmetric with respect to the ...
متن کاملOn the Moduli Spaces of Embedded Constant Mean Curvature Surfaces with Three or Four Ends
We are interested in explicitly parametrizing the moduli spaces Mg,k of embedded surfaces in R with finite genus g and a finite number of ends k having constant mean curvature. By rescaling we may assume this constant is 1, the mean curvature of the unit sphere. Two surfaces in R are indentified as points inMg,k if there is isometry of R carrying one surface to the other. Moreover, we shall inc...
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The study of constant mean curvature surfaces in a space-form has been an active field since the work of H. Hopf in the 1920’s and H.Liebmann in the years around 1900. The questions which are generally of interest are global questions of existence and uniqueness in complete 3-manifolds. We deal in this short paper on a question of existence and uniqueness with respect to the complex structure a...
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ژورنال
عنوان ژورنال: Geometric and Functional Analysis
سال: 1996
ISSN: 1016-443X,1420-8970
DOI: 10.1007/bf02246769