Search results for "funktioteoria"
showing 10 items of 39 documents
Weighted estimates for diffeomorphic extensions of homeomorphisms
2019
Let $\Omega \subset \mbr^2$ be an internal chord-arc domain and $\varphi : \mbs^1 \rightarrow \partial \Omega$ be a homeomorphism. Then there is a diffeomorphic extension $h : \mbd \rightarrow \Omega$ of $\varphi .$ We study the relationship between weighted integrability of the derivatives of $h$ and double integrals of $\varphi$ and of $\varphi^{-1} .$
On the notion of parallel transport on RCD spaces
2019
We propose a general notion of parallel transport on RCD spaces, prove an unconditioned uniqueness result and existence under suitable assumptions on the space. peerReviewed
Approximation by uniform domains in doubling quasiconvex metric spaces
2020
We show that any bounded domain in a doubling quasiconvex metric space can be approximated from inside and outside by uniform domains.
The Choquet and Kellogg properties for the fine topology when $p=1$ in metric spaces
2017
In the setting of a complete metric space that is equipped with a doubling measure and supports a Poincar´e inequality, we prove the fine Kellogg property, the quasi-Lindel¨of principle, and the Choquet property for the fine topology in the case p = 1. Dans un contexte d’espace m´etrique complet muni d’une mesure doublante et supportant une in´egalit´e de Poincar´e, nous d´emontrons la propri´et´e fine de Kellogg, le quasi-principe de Lindel¨of, et la propri´et´e de Choquet pour la topologie fine dans le cas p = 1. peerReviewed
Sobolev Extension on Lp-quasidisks
2021
AbstractIn this paper, we study the Sobolev extension property of Lp-quasidisks which are the generalizations of classical quasidisks. After that, we also find some applications of this property.
Quasispheres and metric doubling measures
2018
Applying the Bonk-Kleiner characterization of Ahlfors 2-regular quasispheres, we show that a metric two-sphere $X$ is a quasisphere if and only if $X$ is linearly locally connected and carries a weak metric doubling measure, i.e., a measure that deforms the metric on $X$ without much shrinking.
Admissibility versus Ap-Conditions on Regular Trees
2020
We show that the combination of doubling and (1, p)-Poincaré inequality is equivalent to a version of the Ap-condition on rooted K-ary trees. peerReviewed
Riemann surfaces and Teichmüller theory
2017
Riemannin pinnat ja Teichmüller-teoriaa. Tämän työn päämääränä on määritellä Riemannin pintojen Teichmüller-avaruudet sekä tutkia niiden geometrisia ominaisuuksia. Ensin työssä kehitetään peiteavaruuksien ja toimintojen teoriaa, jota sovelletaan Möbius-kuvauksista koostuviin ryhmiin. Tämän jälkeen kvasikonformaalikuvaukset määritellään Riemannin pinnoille ja niiden yhteyttä yhdesti yhtenäisten Riemannin avaruuksien kvasikonformikuvauksiin tutkitaan. Näitä tietoja sekä yhdesti yhtenäisten Riemannin pintojen uniformisaatiolausetta hyödyntämällä todistetaan yleisten Riemannin pintojen uniformisaatiolause. Tämä tulos liittää pinnat Möbius-kuvauksien toimintoihin yhdesti yhtenäisillä Riemannin p…
Stoïlow’s theorem revisited
2020
Stoilow's theorem from 1928 states that a continuous, open, and light map between surfaces is a discrete map with a discrete branch set. This result implies that such maps between orientable surfaces are locally modeled by power maps z -> z(k) and admit a holomorphic factorization. The purpose of this expository article is to give a proof of this classical theorem having readers in mind that are interested in continuous, open and discrete maps. (C) 2019 Elsevier GmbH. All rights reserved. Peer reviewed
Quasiconformal geometry and removable sets for conformal mappings
2020
We study metric spaces defined via a conformal weight, or more generally a measurable Finsler structure, on a domain $\Omega \subset \mathbb{R}^2$ that vanishes on a compact set $E \subset \Omega$ and satisfies mild assumptions. Our main question is to determine when such a space is quasiconformally equivalent to a planar domain. We give a characterization in terms of the notion of planar sets that are removable for conformal mappings. We also study the question of when a quasiconformal mapping can be factored as a 1-quasiconformal mapping precomposed with a bi-Lipschitz map.