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Harmonic mappings in the exterior of the unit disk

100%

Gregorczyk M., Widomski J.

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

2010

tom 64

nr 1

In this paper we consider a class of univalent orientation-preserving harmonic functions defined on the exterior of the unit disk which satisfy the condition\(\sum_{n=1}^{\infty}n^{p}(|a_{n}|+|b_{n}|)\leq 1\). We are interested in finding radius of univalence and convexity for such class and we find extremal functions. Convolution, convex combination, and explicit quasiconformal extension for this class are also determined.

Univalent functions with logarithmic restrictions

86%

Grinshpan A.

Annales Polonici Mathematici

1991

tom 55

nr 1

117-139

It is known that univalence property of regular functions is better understood in terms of some restrictions of logarithmic type. Such restrictions are connected with natural stratifications of the studied classes of univalent functions. The stratification of the basic class S of functions regular and univalent in the unit disk by the Grunsky operator norm as well as the more general one of the class 𝔐 * of pairs of univalent functions without common values by the τ-norm (this concept is introduced here) are given in the paper. Moreover, some properties of univalent functions whose range has finite logarithmic area are considered. To apply the logarithmic restrictions a special exponentiation technique is used.

The harmonic and quasiconformal extension operators

58%

Partyka D., Sakan K.-I., Zając J.

Banach Center Publications

1999

tom 48

nr 1

141-177

Different aspects of the boundary value problem for quasiconformal mappings and Teichmüller spaces are expressed in a unified form by the use of the trace and extension operators. Moreover, some new results on harmonic and quasiconformal extensions are included.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

1 Banach Center Publications

1 Gregorczyk M.

1 Grinshpan A.

1 Partyka D.

1 Sakan K.-I.

1 Widomski J.

1 Zając J.

1 2010

1 1999

1 1991

Wyniki wyszukiwania

Harmonic mappings in the exterior of the unit disk

Univalent functions with logarithmic restrictions

The harmonic and quasiconformal extension operators