Given a domain $\Omega $ of ${\mathbb{R}}^{m+1}$ 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.

@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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