Constant Mean Curvature Hypersurfaces in S by Gluing Spherical Building Blocks

Constant mean curvature hypersurfaces in S n + 1 by gluing spherical building blocks

The techniques developed by Butscher (Gluing constructions amongst constant mean curvature hypersurfaces of Sn+1) for constructing constant mean curvature (CMC) hypersurfaces in Sn+1 by gluing together spherical building blocks are generalized to handle less symmetric initial configurations. The outcome is that the approximately CMC hypersurface obtained by gluing the initial configuration toge...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Linear Weingarten hypersurfaces in a unit sphere

In this paper, by modifying Cheng-Yau$'$s technique to complete hypersurfaces in $S^{n+1}(1)$, we prove a rigidity theorem under the hypothesis of the mean curvature and the normalized scalar curvature being linearly related which improve the result of [H. Li, Hypersurfaces with constant scalar curvature in space forms, {em Math. Ann.} {305} (1996), 665--672].  

Generalized Doubling Constructions for Constant Mean Curvature Hypersurfaces in S

The sphere S contains a simple family of constant mean curvature (CMC) hypersurfaces of the form Λp,q a ≡ S p(a)×Sq( √ 1− a) for p+ q+1 = n and a ∈ (0, 1) called the generalized Clifford hypersurfaces. This paper demonstrates that new, topologically non-trivial CMC hypersurfaces resembling a pair of neighbouring generalized Clifford tori connected to each other by small catenoidal bridges at a ...

A Gluing Construction for Prescribed Mean Curvature

The gluing technique is used to construct hypersurfaces in Euclidean space having approximately constant prescribed mean curvature. These surfaces are perturbations of unions of finitely many spheres of the same radius assembled end-to-end along a line segment. The condition on the existence of these hypersurfaces is the vanishing of the sum of certain integral moments of the spheres with respe...