Displaying similar documents to “Analytic functions in a lacunary end of a Riemann surface”

On separately subharmonic functions (Lelong’s problem)

A. Sadullaev (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

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The main result of the present paper is : every separately-subharmonic function u ( x , y ) , which is harmonic in y , can be represented locally as a sum two functions, u = u * + U , where U is subharmonic and u * is harmonic in y , subharmonic in x and harmonic in ( x , y ) outside of some nowhere dense set S .

On Φ -bounded harmonic functions

Mitsuru Nakai (1966)

Annales de l'institut Fourier

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Soit Φ une fonction non négative réelle ; une fonction u harmonique sur une surface de Riemann R est dite Φ -bornée si Φ ( | u | ) admet une majorante harmonique. On étudie la classe H Φ ( R ) des fonctions Φ -bornées sur R et on montre, en particulier, que chaque u de H Φ ( R ) est essentiellement positive pour toute R , si et seulement si inf t → ∞ Φ ( t ) / t > 0 .

Complex Ginzburg-Landau equations in high dimensions and codimension two area minimizing currents

Fanghua Lin, Tristan Rivière (1999)

Journal of the European Mathematical Society

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There is an obvious topological obstruction for a finite energy unimodular harmonic extension of a S 1 -valued function defined on the boundary of a bounded regular domain of R n . When such extensions do not exist, we use the Ginzburg-Landau relaxation procedure. We prove that, up to a subsequence, a sequence of Ginzburg-Landau minimizers, as the coupling parameter tends to infinity, converges to a unimodular harmonic map away from a codimension-2 minimal current minimizing the area within...

On the boundary limits of harmonic functions with gradient in L p

Yoshihiro Mizuta (1984)

Annales de l'institut Fourier

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This paper deals with tangential boundary behaviors of harmonic functions with gradient in Lebesgue classes. Our aim is to extend a recent result of Cruzeiro (C.R.A.S., Paris, 294 (1982), 71–74), concerning tangential boundary limits of harmonic functions with gradient in L n ( R + n ) , R + n denoting the upper half space of the n -dimensional euclidean space R n . Our method used here is different from that of Nagel, Rudin and Shapiro (Ann. of Math., 116 (1982), 331–360); in fact, we use the integral representation...

On the order of starlikeness and convexity of complex harmonic functions with a two-parameter coefficient condition

Agnieszka Sibelska (2010)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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The article of J. Clunie and T. Sheil-Small [3], published in 1984, intensified the investigations of complex functions harmonic in the unit disc Δ . In particular, many papers about some classes of complex mappings with the coefficient conditions have been published. Consideration of this type was undertaken in the period 1998–2004 by Y. Avci and E. Złotkiewicz [2], A. Ganczar [5], Z. J. Jakubowski, G. Adamczyk, A. Łazinska and A. Sibelska [1], [8], [7], H. Silverman [12] and J. M. Jahangiri...

A non probabilistic proof of the relative Fatou theorem

J. L. Doob (1959)

Annales de l'institut Fourier

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L’auteur démontre en s’appuyant sur la thèse de Mlle Naïm le résultat suivant qu’il avait établi grâce aux probabilités : dans un espace de Green, si u et h sont surharmoniques > 0 , u / h admet en tout point de l’espace ou de sa frontière de Martin une “limite fine” finie, sauf sur un ensemble de mesure nulle pour la mesure associée canoniquement à h . Puis, il peut même affaiblir l’hypothèse u > 0 .

The Martin boundaries of equivalent sheaves

John C. Taylor (1970)

Annales de l'institut Fourier

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The Martin compactification of X defined by a Brelot sheaf H 1 satisfying proportionality is shown to be the same as for H 2 if the sheaves agree outside a compact set. Minimal points coincide and hence S 1 + and S 2 + are isomorphic topological cones. Nakai’s result on the extension to X of a function harmonic outside a compact set is extended to Bauer’s theory. The connected components of the Martin boundary Δ correspond to the ends of X which are related to direct decomposition of the cone H + . ...