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, p. 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 : 2019-02-22
Classification:  53A10,  35J93,  35B25
@article{ASNSP_2012_5_11_3_653_0,
     author = {Butscher, Adrian and Mazzeo, Rafe},
     title = {CMC hypersurfaces condensing to geodesic segments and rays in Riemannian manifolds},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 11},
     number = {3},
     year = {2012},
     pages = {653-706},
     zbl = {1260.53111},
     mrnumber = {3059841},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2012_5_11_3_653_0}
}
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://www.numdam.org/item/ASNSP_2012_5_11_3_653_0/

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