%0 Journal Article
%T Constant Mean Curvature Hypersurfaces Condensing to Geodesic Segments and Rays in Riemannian Manifolds
%A Adrian Butscher
%A Rafe Mazzeo
%J Mathematics
%D 2008
%I arXiv
%X We construct examples of compact and one-ended constant mean curvature surfaces with large mean curvature in Riemannian manifolds with axial symmetry by gluing together small spheres positioned end-to-end along a geodesic. Such surfaces cannot exist in Euclidean space, but we show that the gradient of the ambient scalar curvature acts as a `friction term' which permits the usual analytic gluing construction to be carried out.
%U http://arxiv.org/abs/0812.3133v1