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

Mouhamed Moustapha Fall; Fethi Mahmoudi

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2008)

  • Volume: 7, Issue: 3, page 407-446
  • ISSN: 0391-173X

Abstract

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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.

How to cite

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Fall, Mouhamed Moustapha, and Mahmoudi, Fethi. "Hypersurfaces with free boundary and large constant mean curvature: concentration along submanifolds." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 7.3 (2008): 407-446. <http://eudml.org/doc/272255>.

@article{Fall2008,
abstract = {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.},
author = {Fall, Mouhamed Moustapha, Mahmoudi, Fethi},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {3},
pages = {407-446},
publisher = {Scuola Normale Superiore, Pisa},
title = {Hypersurfaces with free boundary and large constant mean curvature: concentration along submanifolds},
url = {http://eudml.org/doc/272255},
volume = {7},
year = {2008},
}

TY - JOUR
AU - Fall, Mouhamed Moustapha
AU - Mahmoudi, Fethi
TI - Hypersurfaces with free boundary and large constant mean curvature: concentration along submanifolds
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2008
PB - Scuola Normale Superiore, Pisa
VL - 7
IS - 3
SP - 407
EP - 446
AB - 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.
LA - eng
UR - http://eudml.org/doc/272255
ER -

References

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