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

Fall, Mouhamed Moustapha; Mahmoudi, Fethi

Geodesic

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

Fall, Mouhamed Moustapha ; Mahmoudi, Fethi

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 7 (2008) no. 3, pp. 407-446

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Résumé

Given a domain $Ω$ of $ℝ^{m + 1}$ and a $k$ -dimensional non-degenerate minimal submanifold $K$ of $\partial Ω$ with $1 \leq k \leq m - 1$ , 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 $\partial Ω$ perpendicularly along their boundaries.

MR Zbl

Classification : 53A10, 53C21, 35R35

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     author = {Fall, Mouhamed Moustapha and Mahmoudi, Fethi},
     title = {Hypersurfaces with free boundary and large constant mean curvature: concentration along submanifolds},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {407--446},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 7},
     number = {3},
     year = {2008},
     mrnumber = {2466435},
     zbl = {1171.53010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ASNSP_2008_5_7_3_407_0/}
}

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Fall, Mouhamed Moustapha; Mahmoudi, Fethi. Hypersurfaces with free boundary and large constant mean curvature: concentration along submanifolds. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 7 (2008) no. 3, pp. 407-446. http://geodesic.mathdoc.fr/item/ASNSP_2008_5_7_3_407_0/