CMC hypersurfaces condensing to Geodesic segments and rays in Riemannian manifolds

• Adrian Butscher ^[1] ; Rafe Mazzeo ^[1]
  1. [1] Stanford University

     Stanford University

     Estados Unidos

     
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 11, Nº 3, 2012, págs. 653-706
• Idioma: inglés
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• Resumen

  • 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.