On the constructibility of a negatively curved complete surface of constant mean curvature in \(\mathbb{H}^3\) determined by a prescribed Hopf differential
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Publication:1407763
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
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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