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math.MG2026
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…
math.MG2020
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…
math.MG2020
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…