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

Mouhamed Moustapha Fall;  Fethi Mahmoudi — 2008

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Given a domain Ω of ℝ 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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