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Hypersurfaces with free boundary and large constant mean curvature: concentration along submanifolds

Mouhamed Moustapha FallFethi Mahmoudi — 2008

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Given a domain Ω of m + 1 and a k -dimensional non-degenerate minimal submanifold K of Ω with 1 k m - 1 , we prove the existence of a family of embedded constant mean curvature hypersurfaces in Ω which as their mean curvature tends to infinity concentrate along K and intersecting Ω perpendicularly along their boundaries.

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