CMC hypersurfaces condensing to geodesic segments and rays in Riemannian manifolds
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 11 (2012) no. 3, pp. 653-706.

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.

Published online:
Classification: 53A10, 35J93, 35B25
Butscher, Adrian 1; Mazzeo, Rafe 1

1 Department of Mathematics Stanford University Stanford, CA 94305 USA
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Butscher, Adrian; Mazzeo, Rafe. CMC hypersurfaces condensing to geodesic segments and rays in Riemannian manifolds. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 11 (2012) no. 3, pp. 653-706. http://archive.numdam.org/item/ASNSP_2012_5_11_3_653_0/

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