A characterization of harmonic sections and a Liouville theorem

Simão Stelmastchuk

Displaying similar documents to “A characterization of harmonic sections and a Liouville theorem”

Harmonic morphisms and subharmonic functions.

Choi, Gundon, Yun, Gabjin (2005)

International Journal of Mathematics and Mathematical Sciences

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Stochastic methods and differential geometry

K. David Elworthy (1980-1981)

Séminaire Bourbaki

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Harmonic morphisms and circle actions on 3- and 4-manifolds

Paul Baird (1990)

Annales de l'institut Fourier

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Harmonic morphisms are considered as a natural generalization of the analytic functions of Riemann surface theory. It is shown that any closed analytic 3-manifold supporting a non-constant harmonic morphism into a Riemann surface must be a Seifert fibre space. Harmonic morphisms $ϕ : M \to N$ from a closed 4-manifold to a 3-manifold are studied. These determine a locally smooth circle action on $M$ with possible fixed points. This restricts the topology of $M$ . In all cases, a harmonic morphism $ϕ : M \to N$ from...

Harmonic morphisms between riemannian manifolds

Bent Fuglede (1978)

Annales de l'institut Fourier

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A harmonic morphism $f : M \to N$ between Riemannian manifolds $M$ and $N$ is by definition a continuous mappings which pulls back harmonic functions. It is assumed that dim $M \geq$ 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...

Stochastic harmonic morphisms : functions mapping the paths of one diffusion into the paths of another

Bernt Oksendal, L. Csink (1983)

Annales de l'institut Fourier

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We give several necessary and sufficient conditions that a function $φ$ maps the paths of one diffusion into the paths of another. One of these conditions is that $φ$ is a harmonic morphism between the associated harmonic spaces. Another condition constitutes an extension of a result of P. Lévy about conformal invariance of Brownian motion. The third condition implies that two diffusions with the same hitting distributions differ only by a chance of time scale. We also obtain a converse...

Boundary behaviour of harmonic functions in a half-space and brownian motion

D. L. Burkholder, Richard F. Gundy (1973)

Annales de l'institut Fourier

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Let $u$ be harmonic in the half-space $R_{+}^{n + 1}$ , $n \geq 2$ . We show that $u$ can have a fine limit at almost every point of the unit cubs in $R^{n} = \partial R_{+}^{n + 1}$ but fail to have a nontangential limit at any point of the cube. The method is probabilistic and utilizes the equivalence between conditional Brownian motion limits and fine limits at the boundary. In $R_{+}^{2}$ it is known that the Hardy classes $H^{p}$ , $0 < p < \infty$ , may be described in terms of the integrability of the nontangential maximal function, or, alternatively, in terms...