Displaying similar documents to “The angular distribution of mass by Bergman functions.”

Hyperbolic singular integral operators.

Andrea R. Nahmod (1995)

Revista Matemática Iberoamericana

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We define a class of integral operators which are singular relative to the hyperbolic metric in simply connected domains of the plane. We study the necessary and sufficient conditions for such operators to be bounded on L of the upper half plane relative to the hyperbolic metric.

Generalized John disks

Chang-Yu Guo, Pekka Koskela (2014)

Open Mathematics

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We establish the basic properties of the class of generalized simply connected John domains.

Combinatorial Modulus on Boundary of Right-Angled Hyperbolic Buildings

Antoine Clais (2016)

Analysis and Geometry in Metric Spaces

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In this article, we discuss the quasiconformal structure of boundaries of right-angled hyperbolic buildings using combinatorial tools. In particular, we exhibit some examples of buildings of dimension 3 and 4 whose boundaries satisfy the combinatorial Loewner property. This property is a weak version of the Loewner property. This is motivated by the fact that the quasiconformal structure of the boundary led to many results of rigidity in hyperbolic spaces since G.D.Mostow. In the case...

Hyperbolically convex functions

Wancang Ma, David Minda (1994)

Annales Polonici Mathematici

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We investigate univalent holomorphic functions f defined on the unit disk 𝔻 such that f(𝔻) is a hyperbolically convex subset of 𝔻; there are a number of analogies with the classical theory of (euclidean) convex univalent functions. A subregion Ω of 𝔻 is called hyperbolically convex (relative to hyperbolic geometry on 𝔻) if for all points a,b in Ω the arc of the hyperbolic geodesic in 𝔻 connecting a and b (the arc of the circle joining a and b which is orthogonal to the unit circle)...