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math.DG2013
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…
math.DG2013★ 1 cited
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…