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Displaying similar documents to “On coefficients, boundary size and Hölder domains.”

On the Residuum of Concave Univalent Functions

Wirths, K.-J. (2006)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 30C25, 30C45. Let D denote the open unit disc and f:D→[`C] be meromorphic and injective in D. We further assume that f has a simple pole at the point p О (0,1) and is normalized by f(0) = 0 and f′(0) = 1. In particular, we are concerned with f that map D onto a domain whose complement with respect to [`C] is convex. Because of the shape of f(D) these functions will be called concave univalent functions with pole p and the family of...

The Lowner-Kufarev representations for domains with analytic boundaries

Dmitri Prokhorov (2011)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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We consider the Lowner-Kufarev differential equations generating univalent maps of the unit disk onto domains bounded by analytic Jordan curves. A solution to the problem of the maximal lifetime shows how long a representation of such functions admits using infinitesimal generators analytically extendable outside the unit disk. We construct a Lowner-Kufarev chain consisting of univalent quadratic polynomials and compare the Lowner-Kufarev representations of bounded and arbitrary univalent...

The Löwner-Kufarev representations for domains with analytic boundaries

Dmitri Prokhorov (2011)

Annales UMCS, Mathematica

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We consider the Löwner-Kufarev differential equations generating univalent maps of the unit disk onto domains bounded by analytic Jordan curves. A solution to the problem of the maximal lifetime shows how long a representation of such functions admits using infinitesimal generators analytically extendable outside the unit disk. We construct a Löwner-Kufarev chain consisting of univalent quadratic polynomials and compare the Löwner-Kufarev representations of bounded and arbitrary univalent...

Boundary subordination

Adam Lecko (2012)

Annales Polonici Mathematici

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We study the idea of the boundary subordination of two analytic functions. Some basic properties of the boundary subordination are discussed. Applications to classes of univalent functions referring to a boundary point are demonstrated.