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Displaying 21 – 40 of 127

The boundary absolute continuity of quasiconformal mappings (II).

Juha Heinonen (1996)

Revista Matemática Iberoamericana

In this paper a quite complete picture is given of the absolute continuity on the boundary of a quasiconformal map B3 → D, where B3 is the unit 3-ball and D is a Jordan domain in R3 with boundary 2-rectifiable in the sense of geometric measure theory. Moreover, examples are constructed, for each n ≥ 3, showing that quasiconformal maps from the unit n-ball onto Jordan domains with boundary (n - 1)-rectifiable need not have absolutely continuous boundary values.

The Brothers Riesz theorem in $ℝ^{n}$ and Laplace series.

Cialdea, A. (1997)

Memoirs on Differential Equations and Mathematical Physics

The Carathéodory topology for multiply connected domains I

Mark Comerford (2013)

Open Mathematics

We consider the convergence of pointed multiply connected domains in the Carathéodory topology. Behaviour in the limit is largely determined by the properties of the simple closed hyperbolic geodesics which separate components of the complement. Of particular importance are those whose hyperbolic length is as short as possible which we call meridians of the domain. We prove continuity results on convergence of such geodesics for sequences of pointed hyperbolic domains which converge in the Carathéodory...

The Carathéodory topology for multiply connected domains II

Mark Comerford (2014)

Open Mathematics

We continue our exposition concerning the Carathéodory topology for multiply connected domains which we began in [Comerford M., The Carathéodory topology for multiply connected domains I, Cent. Eur. J. Math., 2013, 11(2), 322–340] by introducing the notion of boundedness for a family of pointed domains of the same connectivity. The limit of a convergent sequence of n-connected domains which is bounded in this sense is again n-connected and will satisfy the same bounds. We prove a result which establishes...

The Cauchy Kernel, the Szegö Kernel, and the Riemann Mapping Function.

N. Kerzman, E.M. Stein (1978)

Mathematische Annalen

The class of functions convex in the negative direction of the imaginary axis of order $(α, β)$ .

Lecko, Adam (2002)

International Journal of Mathematics and Mathematical Sciences

The class of functions spirallike with respect to a boundary point.

Lecko, Adam (2004)

International Journal of Mathematics and Mathematical Sciences

The class of mappings with bounded specific oscillation, and integrability of mappings with bounded distortion on Carnot groups.

Isangulova, D.V. (2007)

Sibirskij Matematicheskij Zhurnal

The classes of univalent functions connected with homographies

Kajetan Tochowicz (1991)

Annales Polonici Mathematici

We define some new classes of univalent functions. The Schiffer differential equations are obtained for extremal functions from some of these classes.

The coefficient problem for functions with positive real part in a finitely connected domain

Helmut Grunsky (1983)

Banach Center Publications

The coefficients of quasiconformality of tori in n-space.

Kari Hag (1980)

Commentarii mathematici Helvetici

The complement of a quasimöbius sphere is uniform.

MacManus, Paul (1996)

Annales Academiae Scientiarum Fennicae. Mathematica

The cone of nonnegative polynomials with nonnegative coefficients and linear operators preserving this cone

Olga Katkova, Anna Vishnyakova (2014)

Open Mathematics

Let be the cone of real univariate polynomials of degree ≤ 2n which are nonnegative on the real axis and have nonnegative coefficients. We describe the extremal rays of this convex cone and the class of linear operators, acting diagonally in the standard monomial basis, preserving this cone.

The covering radius of a mapping and the multiplicity of a covering.

Semenov, V.I. (2001)

Siberian Mathematical Journal

The critical strips of the sums $1 + 2^{z} + \dots + n^{z}$ .

Mora, G., Sepulcre, J.M. (2011)

Abstract and Applied Analysis

The Differential of a Quasi-conformal Mapping of a Carnot-Caratheodry Space.

G.A. Margulies, G.D. Mostow (1995)

Geometric and functional analysis

The Dirichlet space: a survey.

Arcozzi, Nicola, Rochberg, Richard, Sawyer, Eric T., Wick, Brett D. (2011)

The New York Journal of Mathematics [electronic only]

The Douady-Earle extension of quasihomographies

Ken-Ichi Sakan, Józef Zając (1996)

Banach Center Publications

Quasihomography is a useful notion to represent a sense-preserving automorphism of the unit circle T which admits a quasiconformal extension to the unit disc. For K ≥ 1 let $A_{T} (K)$ denote the family of all K-quasihomographies of T. With any $f \in A_{T} (K)$ we associate the Douady-Earle extension $E_{f}$ and give an explicit and asymptotically sharp estimate of the $L_{\infty}$ norm of the complex dilatation of $E_{f}$ .

The dynamical motion of the zeros of the partial sums of $e^{z}$ , and its relationship to discrepancy theory.

Varga, Richard S., Carpenter, Amos J., Lewis, Bryan W. (2008)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

The Dziok-Srivastava operator and $k$ -uniformly starlike functions.

Aghalary, R., Azadi, Gh. (2005)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

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