3 citations · 3 across the 4 of their papers we have counts for
4 papers
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…
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…