End-to-end gluing of constant mean curvature hypersurfaces. (English) Zbl 1206.53010

Jleli, Mohamed

Ann. Fac. Sci. Toulouse, Math. (6) 18, No. 4, 717-737 (2009).

The author proves the following: Given two nondegenerate constant mean curvature (CMC) hypersurfaces with finitely many Delaunay ends. Assume each has an end of necksize \(\tau\). Then the hypersurface formed by gluing their matching ends can be perturbed to a CMC “end-to-end connected sum”. This is one in a series of papers by the author and F. Pacard, which produce non-trivial examples to apply this connected sum to, and study the resulting moduli space. In the case of CMC surfaces, these results were proved by Ratzkin’s in his PHD Thesis.

Reviewer: Ivan C. Sterling (St. Mary’s City)

MSC:

53A10

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature

Keywords:

constant mean curvature; hypersurfaces; end; necksize

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