206 citations · 394 across the 45 of their papers we have counts for
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Interpolated measures with bounded density in metric spaces satisfying the curvature-dimension conditions of Sturm
Tapio Rajala
We construct geodesics in the Wasserstein space of probability measure along which all the measures have an upper bound on their density that is determined by the densities of the…
Slopes of Kantorovich potentials and existence of optimal transport maps in metric measure spaces
Luigi Ambrosio, Tapio Rajala
We study optimal transportation with the quadratic cost function in geodesic metric spaces satisfying suitable non-branching assumptions. We introduce and study the notions of slop…
Local Poincaré inequalities from stable curvature conditions on metric spaces
Tapio Rajala
We prove local Poincaré inequalities under various curvature-dimension conditions which are stable under the measured Gromov-Hausdorff convergence. The first class of spaces we con…
Thin and fat sets for doubling measures in metric spaces
Tuomo Ojala, Tapio Rajala, Ville Suomala
We consider sets in uniformly perfect metric spaces which are null for every doubling measure of the space or which have positive measure for all doubling measures. These sets are…