Surfaces of Constant Mean Curvature Bounded by Convex Curves
نویسنده
چکیده
This paper proves that an embedded compact surface in the Euclidean space with constant mean curvature H 6= 0 bounded by a circle of radius 1 and included in a slab of width 1=jHj is a spherical cap. Also, we give partial answers to the problem when a surface with constant mean curvature and planar boundary lies in one of the halfspaces determined by the plane containing the boundary, exactly, when the surface is included in a slab. Mathematics Subject Classifications (1991): 53A10, 53C42.
منابع مشابه
Surfaces of Constant Mean Curvature Bounded by Two Planar Curves ? RAFAEL LÓPEZ
In this paper we study constant mean curvature compact surfaces with two Jordan curves in parallel planes as boundary and we investigate the point at which the surface inherits the symmetries of its boundary.
متن کاملPROPERLY EMBEDDED SURFACES WITH CONSTANT MEAN CURVATURE By ANTONIO ROS and HAROLD ROSENBERG
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 کاملProperly 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 ...
متن کاملStructure Theorems for Constant Mean Curvature Surfaces Bounded by a Planar Curve
3 is the boundary of two spherical caps of constant mean curvature H for any positive number H, which is at most the radius of C. It is natural to ask whether spherical caps are the only possible examples. Some examples of constant mean curvature immersed tori by Wente [7] indicate that there are compact genus-one immersed constant mean curvature surfaces with boundary C that are approximated b...
متن کاملConstant 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....
متن کامل