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Infinitesimal Hilbertianity of Locally $$\mathrm{CAT}(\kappa )$$-Spaces

Di Marino, Simone ; Gigli, Nicola ; Pasqualetto, Enrico ; Soultanis, Elefterios

In: The Journal of Geometric Analysis, 2020, p. -

Maximal metric surfaces and the Sobolev-to-Lipschitz property

Creutz, Paul ; Soultanis, Elefterios

In: Calculus of Variations and Partial Differential Equations, 2020, vol. 59, no. 5, p. 177

We find maximal representatives within equivalence classes of metric spheres. For Ahlfors regular spheres these are uniquely characterized by satisfying the seemingly unrelated notions of Sobolev-to-Lipschitz property, or volume rigidity. We also apply our construction to solutions of the Plateau problem in metric spaces and obtain a variant of the associated intrinsic disc studied by...

Metric currents and polylipschitz forms

Pankka, Pekka ; Soultanis, Elefterios

In: Calculus of Variations and Partial Differential Equations, 2020, vol. 59, no. 2, p. 76

Differential of metric valued Sobolev maps

Gigli, Nicola ; Pasqualetto, Enrico ; Soultanis, Elefterios

In: Journal of Functional Analysis, 2020, vol. 278, no. 6, p. 108403

We introduce a notion of differential of a Sobolev map between metric spaces. The differential is given in the framework of tangent and cotangent modules of metric measure spaces, developed by the first author. We prove that our notion is consistent with Kirchheim's metric differential when the source is a Euclidean space, and with the abstract differential provided by the first author when...