206 citations · 394 across the 45 of their papers we have counts for
4 papers · 1 filter
Assouad dimension, Nagata dimension, and uniformly close metric tangents
Enrico Le Donne, Tapio Rajala
We study the Assouad dimension and the Nagata dimension of metric spaces. As a general result, we prove that the Nagata dimension of a metric space is always bounded from above by…
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…
Euclidean spaces as weak tangents of infinitesimally Hilbertian metric spaces with Ricci curvature bounded below
Nicola Gigli, Andrea Mondino, Tapio Rajala
We show that in any infinitesimally Hilbertian -space at almost every point there exists a Euclidean weak tangent, i.e. there exists a sequence of dilations of the space…