Geodesic
CMC hypersurfaces condensing to geodesic segments and rays in Riemannian manifolds
Butscher, Adrian1 ; Mazzeo, Rafe1
1 Department of Mathematics Stanford University Stanford, CA 94305 USA
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 11 (2012) no. 3, pp. 653-706

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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.

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Classification : 53A10, 35J93, 35B25

Butscher, Adrian 1 ; Mazzeo, Rafe 1

1 Department of Mathematics Stanford University Stanford, CA 94305 USA 
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     title = {CMC hypersurfaces condensing to geodesic segments and rays in {Riemannian} manifolds},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
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     publisher = {Scuola Normale Superiore, Pisa},
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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, Série 5, Tome 11 (2012) no. 3, pp. 653-706. http://geodesic.mathdoc.fr/item/ASNSP_2012_5_11_3_653_0/