3 citations · 3 across the 11 of their papers we have counts for
12 papers
Systolic inequalities for metric surfaces via filling minimality
Toni Ikonen, Denis Marti, Noa Vikman
We prove optimal systolic inequalities for length spaces homeomorphic to a torus of genus one or a real projective plane. In both cases, the optimal constant coincides with the con…
Metric Sobolev spaces II: dual energies and divergence measures
Luigi Ambrosio, Toni Ikonen, Danka Lučić +1
This is the second of two works concerning the Sobolev calculus on metric measure spaces and its applications. In this work, we focus on several approaches to vector calculus in th…
Metric Sobolev spaces I: equivalence of definitions
Luigi Ambrosio, Toni Ikonen, Danka Lučić +1
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…
Pushforward of currents under Sobolev maps
Toni Ikonen
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 integ…
Coarea Inequality for Monotone Functions on Metric Surfaces
Behnam Esmayli, Toni Ikonen, Kai Rajala
We study coarea inequalities for metric surfaces -- metric spaces that are topological surfaces, without boundary, and which have locally finite Hausdorff 2-measure …
Extensions and approximations of Banach-valued Sobolev functions
Miguel García-Bravo, Toni Ikonen, Zheng Zhu
In complete metric measure spaces equipped with a doubling measure and supporting a weak Poincaré inequality, we investigate when a given Banach-valued Sobolev function defined on…
Pullback of a quasiconformal map between arbitrary metric measure spaces
Toni Ikonen, Danka Lučić, Enrico Pasqualetto
We prove that every (geometrically) quasiconformal homeomorphism between metric measure spaces induces an isomorphism between the cotangent modules constructed by Gigli. We obtain…
Two-dimensional metric spheres from gluing hemispheres
Toni Ikonen
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 distan…
Abstract and concrete tangent modules on Lipschitz differentiability spaces
Toni Ikonen, Enrico Pasqualetto, Elefterios Soultanis
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…
Quasiconformal Jordan domains
Toni Ikonen
We extend the classical Carathéodory extension theorem to quasiconformal Jordan domains . We say that a metric space is a quasiconformal Jordan domain…
Quasiconformal geometry and removable sets for conformal mappings
Toni Ikonen, Matthew Romney
We study metric spaces defined via a conformal weight, or more generally a measurable Finsler structure, on a domain that vanishes on a compact set $E \subs…
Uniformization Of Metric Surfaces Using Isothermal Coordinates
Toni Ikonen
We establish a uniformization result for metric surfaces - metric spaces that are topological surfaces with locally finite Hausdorff 2-measure. Using the geometric definition of qu…