Displaying similar documents to “Embedding of open riemannian manifolds by harmonic functions”

Harmonic morphisms between riemannian manifolds

Bent Fuglede (1978)

Annales de l'institut Fourier

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A harmonic morphism f : M → N between Riemannian manifolds M and N is by definition a continuous mappings which pulls back harmonic functions. It is assumed that dim M ≥ dim N , since otherwise every harmonic morphism is constant. It is shown that a harmonic morphism is the same as a harmonic mapping in the sense of Eells and Sampson with the further property of being semiconformal, that is, a conformal submersion of the points where d f vanishes. Every non-constant harmonic morphism is shown to be...

On harmonic vector fields.

Jerzy J. Konderak (1992)

Publicacions Matemàtiques

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A tangent bundle to a Riemannian manifold carries various metrics induced by a Riemannian tensor. We consider harmonic vector fields with respect to some of these metrics. We give a simple proof that a vector field on a compact manifold is harmonic with respect to the Sasaki metric on TM if and only if it is parallel. We also consider the metrics and on a tangent bundle (cf. [YI]) and harmonic vector fields generated by them.

On the Martin compactification of a bounded Lipschitz domain in a riemannian manifold

John C. Taylor (1978)

Annales de l'institut Fourier

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The Martin compactification of a bounded Lipschitz domain D ⊂ R n is shown to be D ‾ for a large class of uniformly elliptic second order partial differential operators on D . Let X be an open Riemannian manifold and let M ⊂ X be open relatively compact, connected, with Lipschitz boundary. Then M ‾ is the Martin compactification of M associated with the restriction to M of the Laplace-Beltrami operator on X . Consequently an open Riemannian manifold X has at most one compactification which...