The structure of complete embedded surfaces with constant mean curvature

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...

Properly embedded surfaces with constant mean curvature

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 ...

The rigidity of embedded constant mean curvature surfaces

We study the rigidity of complete, embedded constant mean curvature surfaces in R 3 . Among other things, we prove that when such a surface has finite genus, then intrinsic isometries of the surface extend to isometries of R 3 or its isometry group contains an index two subgroup of isometries that extend. Mathematics Subject Classification: Primary 53A10, Secondary 49Q05, 53C42

Conformal Structures and Necksizes of Embedded Constant Mean Curvature Surfaces

Let M = Mg,k denote the space of properly (Alexandrov) embedded constant mean curvature (CMC) surfaces of genus g with k (labeled) ends, modulo rigid motions, endowed with the real analytic structure described in [15]. Let P = Pg,k = Rg,k × R+ be the space of parabolic structures over Riemann surfaces of genus g with k (marked) punctures, the real analytic structure coming from the 3g− 3+ k loc...

Surfaces of Constant Mean Curvature