Zobrazeno 1 - 10
of 42
pro vyhledávání: '"Ikonen, Toni"'
Autor:
Ikonen, Toni, Pankka, Pekka
We consider the following extension of the classical Liouville theorem: A calibration $\omega \in \Lambda^n \mathbb{R}^m$, where $3 \le n \le m$, has the Liouville property if a Sobolev mapping $F\colon \Omega \to \mathbb{R}^m$, where $\Omega \subset
Externí odkaz:
http://arxiv.org/abs/2410.02722
Autor:
Ikonen, Toni
We prove a Painlev\'e theorem for bounded quasiregular curves in Euclidean spaces extending removability results for quasiregular mappings due to Iwaniec and Martin. The theorem is proved by extending a fundamental inequality for volume forms to cali
Externí odkaz:
http://arxiv.org/abs/2407.02334
This is the first of two works concerning the Sobolev calculus on metric measure spaces and its applications. In this work, we focus on several notions of metric Sobolev space and on their equivalence. More precisely, we give a systematic presentatio
Externí odkaz:
http://arxiv.org/abs/2404.11190
Autor:
Ikonen, Toni
We prove that a Sobolev map from a Riemannian manifold into a complete metric space pushes forward almost every compactly supported integral current to an Ambrosio--Kirchheim integral current in the metric target, where "almost every" is understood i
Externí odkaz:
http://arxiv.org/abs/2303.15003
In complete metric measure spaces equipped with a doubling measure and supporting a weak Poincar\'e inequality, we investigate when a given Banach-valued Sobolev function defined on a subset satisfying a measure-density condition is the restriction o
Externí odkaz:
http://arxiv.org/abs/2208.12594
We study coarea inequalities for metric surfaces -- metric spaces that are topological surfaces, without boundary, and which have locally finite Hausdorff 2-measure $\mathcal{H}^2$. For monotone Sobolev functions $u\colon X \to \mathbb{R} $, we prove
Externí odkaz:
http://arxiv.org/abs/2208.06185
We prove that every (geometrically) quasiconformal homeomorphism between metric measure spaces induces an isomorphism between the cotangent modules constructed by Gigli. We obtain this by first showing that every continuous mapping $\varphi$ with bou
Externí odkaz:
http://arxiv.org/abs/2112.07795
Autor:
Ikonen, Toni
We study metric spheres Z obtained by gluing two hemispheres of the Euclidean sphere along an orientation-preserving homeomorphism mapping the equator onto itself, where the distance on Z is the canonical distance that is locally isometric to the sph
Externí odkaz:
http://arxiv.org/abs/2106.01295
We construct an isometric embedding from Gigli's abstract tangent module into the concrete tangent module of a space admitting a (weak) Lipschitz differentiable structure, and give two equivalent conditions which characterize when the embedding is an
Externí odkaz:
http://arxiv.org/abs/2011.15092
Autor:
Ikonen, Toni
Publikováno v:
Anal. Geom. Metr. Spaces 2021; 9:167-185
We extend the classical Carath\'eodory extension theorem to quasiconformal Jordan domains $( Y, d_{Y} )$. We say that a metric space $( Y, d_{Y} )$ is a quasiconformal Jordan domain if the completion $\overline{Y}$ of $( Y, d_{Y} )$ has finite Hausdo
Externí odkaz:
http://arxiv.org/abs/2011.07261