Zobrazeno 1 - 10
of 444
pro vyhledávání: '"Vuorinen, Matti"'
We consider constellations of disks which are unions of disjoint hyperbolic disks in the unit disk with fixed radii and unfixed centers. We study the problem of maximizing the conformal capacity of a constellation under constraints on the centers in
Externí odkaz:
http://arxiv.org/abs/2404.19663
We prove an identity which connects the visual angle metric $v_{\mathbb{H}^2}$ and the hyperbolic metric $\rho_{\mathbb{H}^2}$ of the upper half plane $\mathbb{H}^2$. The proof is based on geometric arguments and uses computer algebra methods for for
Externí odkaz:
http://arxiv.org/abs/2404.08942
Publikováno v:
J. Math. Anal. Appl. 539 (2024) 128464
We investigate Lindel\"of and Koebe type boundary behavior results for bounded quasiregular mappings in $n$-dimensional Euclidean space. Our results give sufficient conditions for the existence of non-tangential limits at a boundary point.
Comme
Comme
Externí odkaz:
http://arxiv.org/abs/2401.09164
Autor:
Rainio, Oona, Vuorinen, Matti
Due to the invariance properties of cross-ratio, M\"obius transformations are often used to map a set of points or other geometric object into a symmetric position to simplify a problem studied. However, when the points are mapped under a M\"obius tr
Externí odkaz:
http://arxiv.org/abs/2308.10688
A boundary integral equation method is presented for fast computation of the analytic capacities of compact sets in the complex plane. The method is based on using the Kerzman--Stein integral equation to compute the Szeg\"o kernel and then the value
Externí odkaz:
http://arxiv.org/abs/2307.01808
Using the definition of uniformly perfect sets in terms of convergent sequences, we apply lower bounds for the Hausdorff content of a uniformly perfect subset $E$ of $\mathbb{R}^n$ to prove new explicit lower bounds for the Hausdorff dimension of $E.
Externí odkaz:
http://arxiv.org/abs/2305.16723
We prove several new formulas for the visual angle metric of the unit disk in terms of the hyperbolic metric and apply these to prove a sharp Schwarz lemma for the visual angle metric under quasiregular mappings.
Comment: 15 pages, 9 Figures
Comment: 15 pages, 9 Figures
Externí odkaz:
http://arxiv.org/abs/2304.04485
Autor:
Hinkkanen, Aimo, Vuorinen, Matti
We prove that if $E$ is a compact subset of the unit disk ${\mathbb D}$ in the complex plane, if $E$ contains a sequence of distinct points $a_n\not= 0$ for $n\geq 1$ such that $\lim_{n\to\infty} a_n=0$ and for all $n$ we have $ |a_{n+1}| \geq \frac{
Externí odkaz:
http://arxiv.org/abs/2303.08238
Autor:
Rainio, Oona, Vuorinen, Matti
The Hilbert metric between two points $x,y$ in a bounded convex domain $G$ is defined as the logarithm of the cross-ratio of $x,y$ and the intersection points of the Euclidean line passing through the points $x,y$ and the boundary of the domain. Here
Externí odkaz:
http://arxiv.org/abs/2303.03753
For a fixed integer $m>2$ and $r_j>0, j=1,...,m,$ our focus is to study disjoint disks with hyperbolic radii $r_j$ and the set $E$ which is their union in the hyperbolic space, the unit disk equipped with the hyperbolic metric. Such a set is called a
Externí odkaz:
http://arxiv.org/abs/2303.00145