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This is the second of a series of papers in which we investigate the problem of finding, in hyperbolic space, complete hypersurfaces of constant curvature with a prescribed asymptotic boundary at infinity for a general class of curvature functions. In this paper we focus on graphs over a domain with nonnegative mean curvature.

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

Mouhamed Moustapha Fall, Fethi Mahmoudi (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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.

Displaying 1 – 6 of 6

Hamiltonian flows of curves in G / SO ( N ) and vector soliton equations of mKdV and sine-Gordon type.

Harmonic diffeomorphisms and Teichmüller theory.

Harnack inequalities for curvature flows depending on mean curvature.

Heat content asymptotics for operators to Laplace type with Neumann boundary conditions.

Hypersurfaces of constant curvature in hyperbolic space II

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

Currently displaying 1 – 6 of 6

Hamiltonian flows of curves in $G / SO (N)$ and vector soliton equations of mKdV and sine-Gordon type.