On the constructibility of a negatively curved complete surface of constant mean curvature in \(\mathbb{H}^3\) determined by a prescribed Hopf differential

DOI10.1007/BF02922057zbMath1045.53043OpenAlexW2129917284WikidataQ115391140 ScholiaQ115391140MaRDI QIDQ1407763

Publication date: 10 November 2003

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02922057

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Nonlinear elliptic equations (35J60) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Cites Work

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Unique isometric immersion into hyperbolic space
On the inequality \(\Delta u \geqq f (u)\)
The Gauss map of surfaces in \(\mathbb R^ n\)
All constant mean curvature tori in \(R^ 3\), \(S^ 3\), \(H^ 3\) in terms of theta-functions
Singularities of elliptic equations with an exponential nonlinearity
Conformal deformations of complete manifolds with negative curvature
On the existence of solutions of nonlinear elliptic boundary value problems
Removable singularities for some nonlinear elliptic equations
On the elliptic equation \(\Delta \omega + K(x)e^{2\omega} = 0\) and conformal metrics with prescribed Gaussian curvatures
On symmetries of constant mean curvature surfaces. I: General theory
Kenmotsu-Bryant type representation formulas for constant mean curvature surfaces in \(\mathbb{H}^3 (-c^2)\) and \(\mathbb{S}_1^3 (c^2)\)
`Large' solutions of semilinear elliptic equations: Existence, uniqueness and asymptotic behaviour
Weierstrass representation for minimal surfaces in hyperbolic space
Kenmotsu type representation formula for surfaces with prescribed mean curvature in the 3-sphere
Existence and uniqueness of complete constant mean curvature surfaces at infinity of \({\mathbb{H}}^3\)
Kenmotsu type representation formula for surfaces with prescribed mean curvature in the hyperbolic 3-space
The Dirichlet problem at infinity for harmonic map equations arising from constant mean curvature surfaces in the hyperbolic 3-space
Complete surfaces of constant mean curvature-1 in the hyperbolic 3-space
Ganze Lösungen der Differentialgleichung \(\Delta u=e^u\)
On solutions of δu=f(u)
The hyperbolic Gauss map and quasiconformal reflections.
Complete Metrics Conformal to the Hyperbolic Disc
On the Elliptic Equations Δu = K(x)u σ and Δu = K(x)e 2u
The generalized gauss map of minimal surfaces in H3 and H4
A parametrization of the Weierstrass formulae and perturbation of complete minimal surfaces in R3 into the hyperbolic 3-space.
A Note on Unrestricted Solutions of the Differential Equation Δu =f (u )

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