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Harmonic functions on the real hyperbolic ball I: Boundary values and atomic decomposition of Hardy spaces

Philippe Jaming (1999)

Colloquium Mathematicae

We study harmonic functions for the Laplace-eltrami operator on the real hyperbolic space n . We obtain necessary and sufficient conditions for these functions and their normal derivatives to have a boundary distribution. In doing so, we consider different behaviors of hyperbolic harmonic functions according to the parity of the dimension of the hyperbolic ball n . We then study the Hardy spaces H p ( n ) , 0

Harmonic maps from compact Kähler manifolds with positive scalar curvature to Kähler manifolds of strongly seminegative curvature

Qilin Yang (2009)

Colloquium Mathematicae

It is well known there is no non-constant harmonic map from a closed Riemannian manifold of positive Ricci curvature to a complete Riemannian manifold with non-positive sectional curvature. If one reduces the assumption on the Ricci curvature to one on the scalar curvature, such a vanishing theorem does not hold in general. This raises the question: What information can we obtain from the existence of a non-constant harmonic map? This paper gives an answer to this problem when both manifolds are...

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