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

##### MSC:
 53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
##### Keywords:
constant mean curvature; hypersurfaces; end; necksize
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##### References:
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