scientific article

Publication date: 1981

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

harmonic functions Kleinian groups quasiconformal deformations hyperbolic differential geometry Moebius transformation in several dimensions

Mathematics Subject Classification ID

Hyperbolic and elliptic geometries (general) and generalizations (51M10) Research exposition (monographs, survey articles) pertaining to functions of a complex variable (30-02) Non-Euclidean differential geometry (53A35) Kleinian groups (aspects of compact Riemann surfaces and uniformization) (30F40) Quasiconformal mappings in the complex plane (30C62)

Related Items

Characterization of generalizedperiodic vector fields on hyperbolic space ⋮ Two balls maximize the third Neumann eigenvalue in hyperbolic space ⋮ Invariant mean value property and $\mathcal M$-harmonicity on the half-space ⋮ A “deformation estimate" for the Toeplitz operators on harmonic Bergman spaces ⋮ Bloch space in the unit ball of $\mathbb {C}^{n}$ ⋮ Vector fields with zero flux through circles of fixed radius on $\mathbb{H}^2$ ⋮ Unnamed Item ⋮ Lipschitz type characterizations for Bergman-Orlicz spaces of eigenfunctions on hyperbolic space ⋮ Bianchi and Hilbert-Blumenthal quaternionic orbifolds ⋮ Modified quaternionic analysis on the ball ⋮ Nitsche type inequality for hyperbolic harmonic mappings between annuli in the unit ball $\mathbb{B}^3$ ⋮ Improved Caffarelli-Kohn-Nirenberg inequalities in unit ball and sharp constants in dimension three ⋮ Harmonic Bergman spaces on the real hyperbolic ball: atomic decomposition, interpolation and inclusion relations ⋮ Intrinsic metrics in polygonal domains ⋮ Fundamental solutions for the Laplace-Beltrami operator defined by the conformal hyperbolic metric and Jacobi polynomials ⋮ The Properties of Certain Linear and Nonlinear Differential Equations ⋮ 3d super hyperbolic geometry ⋮ Weighted Dirichlet spaces of harmonic functions on the real hyperbolic ball ⋮ On the Legendre and the Lenstra constants for complex continued fractions introduced by J. Hurwitz ⋮ Diophantine approximation and the geometry of limit sets in Gromov hyperbolic metric spaces ⋮ Hausdorff dimension and conformal measures of Feigenbaum Julia sets ⋮ Series expansion and reproducing kernels for hyperharmonic functions ⋮ Sharp Adams and Hardy-Adams inequalities of any fractional order on hyperbolic spaces of all dimensions ⋮ Groups of line and circle homeomorphisms. Criteria for almost nilpotency ⋮ Conformally invariant inequalities in domains in Euclidean space ⋮ The Poincaré series and the conformal measure of conical and Myrberg limit points ⋮ On quasiregular mappings and domains with a complete conformal metric ⋮ Modified spherical harmonics ⋮ A note on hyperharmonic and polyharmonic functions ⋮ Conformal invariants and quasiregular mappings ⋮ Cosmic time dilation: the clock paradox revisited ⋮ Continued fractions and restrained sequences of Möbius maps ⋮ Fixed points of an integral operator ⋮ Higher dimensional Euclidean and hyperbolic matrix spaces ⋮ The harmonic Bloch and Besov spaces on the real unit ball by an oscillation ⋮ A multi-point Schwarz-Pick lemma ⋮ Recurrent geodesics and controlled concentration points ⋮ The transfinite moduli of condensers in space ⋮ On quasi-inversions ⋮ Harmonic $Q_{p}$-spaces ⋮ On the Lenstra constant associated to the Rosen continued fractions ⋮ On $k$-hypermonogenic functions and their mean value properties ⋮ Hausdorff dimension varies continuously on equivalent dynamically defined wild knots ⋮ Critical Hardy inequality on the half-space via the harmonic transplantation ⋮ A remark on precomposition on $\mathrm H^{1/2}(S^1)$ and $\varepsilon$-identifiability of disks in tomography ⋮ Monogenic Cauchy implies holomorphic Bochner-Martinelli ⋮ On pathwise projective invariance of Brownian motion. III ⋮ Linear gravitational waves and electrodynamic formalism in cosmology ⋮ Fourier analysis and optimal Hardy-Adams inequalities on hyperbolic spaces of any even dimension ⋮ Schwarz-Pick lemma for harmonic and hyperbolic harmonic functions ⋮ Best constants in the Harnack inequality for the Weinstein equation ⋮ Smooth knot limit sets of the complex hyperbolic plane ⋮ Conformal mappings of a once-holed torus ⋮ On the existence of the Legendre constants for some complex continued fraction expansions over imaginary quadratic fields ⋮ The exponent of convergence of Poincaré series associated with some discontinuous groups ⋮ The fractional Carleson measures on the unit ball of $\mathbb R^{n + 1}$ ⋮ Classification of cocycles over ergodic automorphisms with values in the Lorentz group and recurrence of cocycles ⋮ A group of viewpoint changes in the conformal Clifford algebra ⋮ Sharp Hardy-Adams inequalities for bi-Laplacian on hyperbolic space of dimension four ⋮ Hardy-Littlewood inequalities for fractional derivatives of invariant harmonic functions ⋮ Mean value properties for the Weinstein equation using the hyperbolic metric ⋮ Patterson-Sullivan-type measures on Riccati foliations with quasi-Fuchsian holonomy ⋮ Optimal estimates for harmonic functions in the unit ball ⋮ Bergman-type and $Q_k$-type spaces of $p$-harmonic functions ⋮ Hardy spaces and quasiconformal maps in the Heisenberg group ⋮ Weighted reproducing kernels and Toeplitz operators on harmonic Bergman spaces on the real ball ⋮ Operator Lipschitz functions in several variables and Möbius transformations ⋮ On Lipschitz continuity of solutions of hyperbolic Poisson's equation ⋮ Geodesics on quotient manifolds and their corresponding limit points ⋮ Invariant gradient in refinements of Schwarz and Harnack inequalities ⋮ The Fujita exponent for the Cauchy problem in the hyperbolic space ⋮ The Schwarz Lemma for Super-Conformal Maps ⋮ Dimension of escaping geodesics ⋮ On a J. C. C. Nitsche's type inequality for the hyperbolic space $\mathbf H^3$ ⋮ Extreme harmonic functions on a ball ⋮ Carleson measures and conformal self-mappings in the real unit ball ⋮ Normal families of Möbius maps ⋮ Well-posedness of Hersch-Szegő's center of mass by hyperbolic energy minimization ⋮ An alternative to wave mechanics on curved spaces ⋮ Wild knots in higher dimensions as limit sets of Kleinian groups ⋮ Dimension rigidity in conformal structures ⋮ Generalized Bloch spaces, integral means of hyperbolic harmonic mappings in the unit ball ⋮ Quaternionic Kleinian modular groups and arithmetic hyperbolic orbifolds over the quaternions ⋮ Solution to the Khavinson problem near the boundary of the unit ball ⋮ On the construction of the natural extension of the Hurwitz complex continued fraction map ⋮ The Geodesic Flow for Discrete Groups of Infinite Volume ⋮ Double integral characterizations of harmonic Bergman spaces ⋮ Möbius gyrogroups: a Clifford algebra approach. ⋮ A Schwarz lemma for harmonic and hyperbolic-harmonic functions in higher dimensions ⋮ Mean value property and a Berezin-type transform on the half-space ⋮ The pointwise convergence of Möbius maps ⋮ Harmonic maps between 3-dimensional hyperbolic spaces ⋮ The solution operator of the inhomogeneous Dirichlet problem in the unit ball ⋮ Quadruples and spatial quasiconformal mappings ⋮ Weighted harmonic Bloch spaces on the ball ⋮ Iterates of a Berezin-type transform ⋮ Kelvin-Möbius-invariant harmonic function spaces on the real unit ball ⋮ Hardy-Adams inequalities on $\mathbb{H}^2 \times \mathbb{R}^{n-2} $ ⋮ Estimates by gap potentials of free homotopy decompositions of critical Sobolev maps ⋮ Hardy-Sobolev-Maz'ya inequalities for polyharmonic operators ⋮ Electrostatic fields in some special inhomogeneous media and new generalizations of the Cauchy-Riemann system ⋮ Equivalent norms of solutions to hyperbolic Poisson's equations ⋮ Characterizations of the harmonic Bergman space on the ball ⋮ Ping-pong groups and closed geodesics in constant negative curvature ⋮ Invariant mean-value property and $\mathcal M$-harmonicity in the unit ball of $\mathbb{R}^n$ ⋮ Green's functions of Paneitz and GJMS operators on hyperbolic spaces and sharp Hardy-Sobolev-Maz'ya inequalities on half spaces ⋮ Boundary uniqueness theorems for functions whose integrals over hyperbolic discs vanish ⋮ A geometric interpretation of Ungar's addition and of gyration in the hyperbolic plane ⋮ Hecke operators in $KK$-theory and the $K$-homology of Bianchi groups ⋮ Boundary conformal field theories, limit sets of Kleinian groups and holography ⋮ A geometric proof of Mostow's rigidity theorem for groups of divergence type ⋮ Möbius geometry and kinematics in $H^3$ ⋮ Weighted Hölder continuity of hyperbolic harmonic Bloch functions. ⋮ Asymptotic estimates for moduli of extremal rings ⋮ Differentiability and rigidity of Möbius groups ⋮ Quasihyperbolic metric and Möbius transformations ⋮ Harmonic analysis on the Möbius gyrogroup ⋮ A Mourre estimate and related bounds for hyperbolic manifolds with cusps of non-maximal rank ⋮ Discrete conformal groups and measurable dynamics ⋮ Front propagation for nonlinear diffusion equations on the hyperbolic space ⋮ A factorization of a super-conformal map ⋮ Hitting probabilities of killed brownian motion : a study on geometric regularity ⋮ Poincaré series for discrete Moebius groups acting on the upper half space ⋮ Invariant semilinear elliptic equations on manifolds of constant negative curvature ⋮ Higher order Brezis-Nirenberg problem on hyperbolic spaces: existence, nonexistence and symmetry of solutions