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

2007/11/14 by Mouhamed Moustapha Fall, Fall, Mouhamed Moustapha, Fethi Mahmoudi +1
Computer Science · Mathematics · #35R35 #53A10 #53C21 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.0711.2146

openalex publication_date 2007/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a domain Ω of ℝ^m+1 and a k-dimensional non-degenerate minimal submanifold K of \pa Ω with 1≤ k≤ m-1, we prove the existence of a family of embedded constant mean curvature hypersurfaces which as their mean curvature tends to infinity concentrate along K and intersecting ∂ Ω perpendicularly.

Citations

• The existence of surfaces of constant mean curvature with free boundaries
• Existence of Incompressible Minimal Surfaces and the Topology of Three Dimensional Manifolds with Non-Negative Scalar Curvature

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• Constant k-curvature hypersurfaces in Riemannian manifolds
• Min-max theory for constant mean curvature hypersurfaces
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