4 papers
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 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…