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.
@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}, pages = {653--706}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 11}, number = {3}, year = {2012}, mrnumber = {3059841}, zbl = {1260.53111}, language = {en}, url = {http://archive.numdam.org/item/ASNSP_2012_5_11_3_653_0/} }
TY - JOUR AU - Butscher, Adrian AU - Mazzeo, Rafe TI - CMC hypersurfaces condensing to geodesic segments and rays in Riemannian manifolds JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2012 SP - 653 EP - 706 VL - 11 IS - 3 PB - Scuola Normale Superiore, Pisa UR - http://archive.numdam.org/item/ASNSP_2012_5_11_3_653_0/ LA - en ID - ASNSP_2012_5_11_3_653_0 ER -
%0 Journal Article %A Butscher, Adrian %A Mazzeo, Rafe %T CMC hypersurfaces condensing to geodesic segments and rays in Riemannian manifolds %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2012 %P 653-706 %V 11 %N 3 %I Scuola Normale Superiore, Pisa %U http://archive.numdam.org/item/ASNSP_2012_5_11_3_653_0/ %G en %F 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://archive.numdam.org/item/ASNSP_2012_5_11_3_653_0/
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