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Matti Vuorinen

Publications and source records attributed to Matti Vuorinen.

123 records · Page 7Linked to original sources
arXiv2011

Functional inequalities for modified Bessel functions

In this paper our aim is to show some mean value inequalities for the modified Bessel functions of the first and second kinds. Our proofs are based on some bounds for the logarithmic derivatives of these functions, which are in fact equivalent to the corresponding Turán type inequalities for these functions. As an application of the results concerning the modified Bessel function of the second kind we prove that the cumulative distribution function of the gamma-gamma distribution is log-concave. At the end of this paper several open problems are posed, which may be of interest for further research.

math.CA↗
arXiv2010

On moduli of rings and quadrilaterals: algorithms and experiments

Moduli of rings and quadrilaterals are frequently applied in geometric function theory, see e.g. the Handbook by Kühnau. Yet their exact values are known only in a few special cases. Previously, the class of planar domains with polygonal boundary has been studied by many authors from the point of view of numerical computation. We present here a new $hp$-FEM algorithm for the computation of moduli of rings and quadrilaterals and compare its accuracy and performance with previously known methods such as the Schwarz-Christoffel Toolbox of Driscoll and Trefethen. We also demonstrate that the $hp$-FEM algorithm applies to the case of non-polygonal boundary and report results with concrete error bounds.

math.NA↗
arXiv2010

On harmonic quasiconformal quasi-isometries

The purpose of this paper is to explore conditions which guarantee Lipschitz-continuity of harmonic maps w.r.t. quasihyperbolic metrics. For instance, we prove that harmonic quasiconformal maps are Lipschitz w.r.t. quasihyperbolic metrics.

math.CV↗
arXiv2007

Generalized elliptic integrals

Jacobi's elliptic integrals and elliptic functions arise naturally from the Schwarz-Christoffel conformal transformation of the upper half plane onto a rectangle. In this paper we study generalized elliptic integrals which arise from the analogous mapping of the upper half plane onto a quadrilateral and obtain sharp monotonicity and convexity properties for certain combinations of these integrals, thus generalizing analogous well-known results for classical conformal capacity and quasiconformal distortion functions.

math.CA↗
arXiv2007

Geometric properties of quasiconformal maps

Our goal is to provide a survey of some topics in quasiconformal analysis of current interest. We try to emphasize ideas and leave proofs and technicalities aside. Several easily stated open problems are given. Most of the results are joint work with several coauthors.

math.CV↗
arXiv2007

On quasiplanes in Euclidean spaces

A variational inequality for the images of $k$-dimensional hyperplanes under quasiconformal maps of the $n$-dimensional Euclidean space is proved when $1\le k\le n-2 .$

math.CA↗
arXiv2007

Experiments with moduli of quadrilaterals

Basic facts and definitions of conformal moduli of rings and quadrilaterals are recalled. Some computational methods are reviewed. For the case of quadrilaterals with polygonal sides, some recent results are given. Some numerical experiments are presented.

math.NA↗
arXiv2007

Robin functions and distortion theorems for regular mappings

Capacities of generalized condensers are applied to prove a two-point distortion theorem for conformal mappings. The result is expressed in terms of the Robin function and the Robin capacity with respect to the domain of definition of the mapping and subsets of the boundary of this domain. The behavior of Robin function under multivalent functions is studied. Some corollaries and examples of applications to distortion theorems for regular functions are given.

math.CV↗