Zobrazeno 1 - 10
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pro vyhledávání: '"Vuorinen, M."'
We study inequalities between the hyperbolic metric and intrinsic metrics in convex polygonal domains in the complex plane. Special attention is paid to the triangular ratio metric in rectangles. A local study leads to an investigation of the relatio
Externí odkaz:
http://arxiv.org/abs/2206.03744
We study moduli of planar ring domains whose complements are linear segments and establish formulas for their moduli in terms of the Weierstrass elliptic functions. Numerical tests are carried out to illuminate our results.
Comment: 21 pages, 4
Comment: 21 pages, 4
Externí odkaz:
http://arxiv.org/abs/1908.02459
Publikováno v:
J. Aust. Math. Soc. 97 (2014) 383-390
Suppose that $E$ and $E'$ denote real Banach spaces with dimension at least $2$ and that $D\subset E$ and $D'\subset E'$ are domains. In this paper, we establish, in terms of the $j_D$ metric, a necessary and sufficient condition for the homeomorphis
Externí odkaz:
http://arxiv.org/abs/1404.0199
We study the stability of John domains in Banach spaces under removal of a countable set of points. In particular, we prove that the class of John domains is stable in the sense that removing a certain type of closed countable set from the domain yie
Externí odkaz:
http://arxiv.org/abs/1309.6159
Suppose that $E$ and $E'$ denote real Banach spaces with dimension at least 2 and that $D\varsubsetneq E$ and $D'\varsubsetneq E'$ are uniform domains with homogeneously dense boundaries. We consider the class of all $\varphi$-FQC (freely $\varphi$-q
Externí odkaz:
http://arxiv.org/abs/1209.5691
Suppose that $E$ denotes a real Banach space with the dimension at least 2. The main aim of this paper is to show that a domain $D$ in $E$ is a $\psi$-uniform domain if and only if $D\backslash P$ is a $\psi_1$-uniform domain, and $D$ is a uniform do
Externí odkaz:
http://arxiv.org/abs/1206.0128
In this paper, we discuss the minimal surfaces over the slanted half-planes, vertical strips, and single slit whose slit lies on the negative real axis. The representation of these minimal surfaces and the corresponding harmonic mappings are obtained
Externí odkaz:
http://arxiv.org/abs/1204.2890
In this paper, we first study the bounded mean oscillation of planar harmonic mappings, then a relationship between Lipschitz-type spaces and equivalent modulus of real harmonic mappings is established. At last, we obtain sharp estimates on Lipschitz
Externí odkaz:
http://arxiv.org/abs/1202.2183
Autor:
Bhayo, B. A., Vuorinen, M.
This paper deals with generalized elliptic integrals and generalized modular functions. Several new inequalities are given for these and related functions.
Comment: 20 pages, 2 figures
Comment: 20 pages, 2 figures
Externí odkaz:
http://arxiv.org/abs/1102.1078
Autor:
Dubinin, V. N., Vuorinen, M.
Let $E$ be a continuum in the closed unit disk $|z|\le 1$ of the complex $z$-plane which divides the open disk $|z| < 1$ into $n\ge 2$ pairwise non-intersecting simply connected domains $D_k,$ such that each of the domains $D_k$ contains some point $
Externí odkaz:
http://arxiv.org/abs/1011.4178