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• Existence of optimal transport maps in very strict CD(K,∞) -spaces 

  Schultz, Timo (Springer Berlin Heidelberg, 2018)

  We introduce a more restrictive version of the strict CD(K,∞) -condition, the so-called very strict CD(K,∞) -condition, and show the existence of optimal maps in very strict CD(K,∞) -spaces despite the possible ...

• On one-dimensionality of metric measure spaces 

  Schultz, Timo (American Mathematical Society (AMS), 2021)

  In this paper, we prove that a metric measure space which has at least one open set isometric to an interval, and for which the (possibly non-unique) optimal transport map exists from any absolutely continuous measure to ...

• Metric Rectifiability of H-regular Surfaces with Hölder Continuous Horizontal Normal 

  Di Donato, Daniela; Fässler, Katrin; Orponen, Tuomas (Oxford University Press, 2022)

  Two definitions for the rectifiability of hypersurfaces in Heisenberg groups Hn have been proposed: one based on H-regular surfaces and the other on Lipschitz images of subsets of codimension-1 vertical subgroups. The ...

• Indecomposable sets of finite perimeter in doubling metric measure spaces 

  Bonicatto, Paolo; Pasqualetto, Enrico; Rajala, Tapio (Springer, 2020)

  We study a measure-theoretic notion of connectedness for sets of finite perimeter in the setting of doubling metric measure spaces supporting a weak (1,1)-Poincaré inequality. The two main results we obtain are a decomposition ...

• Infinitesimal Hilbertianity of Locally CAT(κ)-Spaces 

  Di Marino, Simone; Gigli, Nicola; Pasqualetto, Enrico; Soultanis, Elefterios (Springer, 2021)

  We show that, given a metric space (Y,d)(Y,d) of curvature bounded from above in the sense of Alexandrov, and a positive Radon measure μμ on YY giving finite mass to bounded sets, the resulting metric measure space ...