206 citations · 394 across the 45 of their papers we have counts for
8 papers · 1 filter
Tensorization of -weak differentiable structures
Sylvester Eriksson-Bique, Tapio Rajala, Elefterios Soultanis
We consider -weak differentiable structures that were recently introduced by the first and last named authors, and prove that the product of -weak charts is a -weak chart.…
Failure of the local-to-global property for CD(K,N) spaces
Tapio Rajala
Given any K and N we show that there exists a compact geodesic metric measure space satisfying locally the CD(0,4) condition but failing CD(K,N) globally. The space with this prope…
Optimal maps and exponentiation on finite dimensional spaces with Ricci curvature bounded from below
Nicola Gigli, Tapio Rajala, Karl-Theodor Sturm
We prove existence and uniqueness of optimal maps on spaces under the assumption that the starting measure is absolutely continuous. We also discuss how this result na…
Non-branching geodesics and optimal maps in strong CD(K,{\infty})-spaces
Tapio Rajala, Karl-Theodor Sturm
We prove that in metric measure spaces where the entropy functional is K-convex along every Wasserstein geodesic any optimal transport between two absolutely continuous measures wi…
Riemannian Ricci curvature lower bounds in metric measure spaces with -finite measure
Luigi Ambrosio, Nicola Gigli, Andrea Mondino +1
Using techniques of optimal transportation and gradient flows in metric spaces, we extend the notion of Riemannian Curvature Dimension condition introduced (in case…
Improved geodesics for the reduced curvature-dimension condition in branching metric spaces
Tapio Rajala
In this note we show that in metric measure spaces satisfying the reduced curvature-dimension condition CD*(K,N) we always have geodesics in the Wasserstein space of probability me…
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…
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…