Harmonic maps on hyperbolic spaces with singular boundary value
نویسندگان
چکیده
منابع مشابه
Harmonic Maps between 3 - Dimensional Hyperbolic Spaces
We prove that a quasiconformal map of the sphere S admits a harmonic quasi-isometric extension to the hyperbolic space H, thus confirming the well known Schoen Conjecture in dimension 3.
متن کاملOn characterizations of hyperbolic harmonic Bloch and Besov spaces
We define hyperbolic harmonic $omega$-$alpha$-Bloch space $mathcal{B}_omega^alpha$ in the unit ball $mathbb{B}$ of ${mathbb R}^n$ and characterize it in terms of $$frac{omegabig((1-|x|^2)^{beta}(1-|y|^2)^{alpha-beta}big)|f(x)-f(y)|}{[x,y]^gamma|x-y|^{1-gamma}},$$ where $0leq gammaleq 1$. Similar results are extended to little $omega$-$alpha$-Bloch and Besov spaces. These obtained...
متن کاملHarmonic Maps between 3 - Dimensional Hyperbolic Spaces Vladimir
We prove that a quasiconformal map of the sphere S admits a harmonic quasi-isometric extension to the hyperbolic space H, thus confirming the well known Schoen Conjecture in dimension 3.
متن کاملHarmonic maps on spaces with conical singularities
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متن کاملHarmonic Maps with Fixed Singular Sets
§ 0. Introduction Here, for a smooth domain Ω in R and a compact smooth Riemannian manifold N we study a space H consisting of all harmonic maps u : Ω → N that have a singular set being a fixed compact subset Z of Ω having finite m− 3 dimensional Minkowski content. This holds if, for example, Z is m− 3 rectifiable [F, 3.2.14]. We define a suitable topology on H using Hölder norms on derivatives...
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ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 1999
ISSN: 0022-040X
DOI: 10.4310/jdg/1214425141