Construction of harmonic maps between pseudo-Riemannian spheres and hyperbolic spaces
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.
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It is shown that smooth maps f : S → S contain two countable families of harmonic representatives in the homotopy classes of degree zero and one.
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 کاملRemovability of singularities of harmonic maps into pseudo-riemannian manifolds
We consider harmonic maps into pseudo-Riemannian manifolds. We show the removability of isolated singularities for continuous maps, i.e. that any continuous map from an open subset of R into a pseudoRiemannian manifold which is two times continuously differentiable and harmonic everywhere outside an isolated point is actually smooth harmonic everywhere. Introduction Given n ∈ N and two nonnegat...
متن کاملSpheres and hyperbolic spaces
The group-invariant geometry on real and complex n-balls is hyperbolic geometry, in the sense that there are infinitely many straight lines (geodesics) through a given point not on a given straight line, thus contravening the parallel postulate for Euclidean geometry. We will not directly consider geometric notions, since the transitive group action determines structure in a more useful form. S...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1990
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1990-0993755-2