Constant Mean Curvature Hypersurfaces Condensing to Geodesic Segments and Rays in Riemannian Manifolds

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/210826We 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.40 pagesDifferential GeometryAnalysis of PDEs53A10Constant Mean Curvature Hypersurfaces Condensing to Geodesic Segments and Rays in Riemannian Manifoldstext