206 citations · 394 across the 45 of their papers we have counts for
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Local multifractal analysis in metric spaces
Antti Käenmäki, Tapio Rajala, Ville Suomala
We study the local dimensions and local multifractal properties of measures on doubling metric spaces. Our aim is twofold. On one hand, we show that there are plenty of multifracta…
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…
Radon-Nikodym property and area formula for Banach homogeneous group targets
Valentino Magnani, Tapio Rajala
We prove a Rademacher-type theorem for Lipschitz mappings from a subset of a Carnot group to a Banach homogeneous group, equipped with a suitably weakened Radon-Nikodym property. W…