Hypersurfaces with free boundary and large constant mean curvature: concentration along submanifolds
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 7 (2008) no. 3, p. 407-446

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

Classification:  53A10,  53C21,  35R35
@article{ASNSP_2008_5_7_3_407_0,
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},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 7},
number = {3},
year = {2008},
pages = {407-446},
zbl = {1171.53010},
mrnumber = {2466435},
language = {en},
url = {http://www.numdam.org/item/ASNSP_2008_5_7_3_407_0}
}

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, Serie 5, Volume 7 (2008) no. 3, pp. 407-446. http://www.numdam.org/item/ASNSP_2008_5_7_3_407_0/

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