- English
- فارسی
6) "Characterization of low dimensional RCD*(K,N) spaces", joint with Y. Kitabeppu, Analysis and Geometry in Metric Spaces 4, 187 215 (2016)
In this paper, we give the characterization of metric measure spaces that satisfy synthetic lower Riemannian Ricci curvature bounds (so called RCD* (K, N) spaces) with non-empty one dimensional regular sets. In particular, we prove that the class of Ricci limit spaces with Ric ≥ K and Hausdorff dimension N and the class of RCD* (K, N) spaces coincide for N < 2 (They can be either complete intervals or circles). We will also prove a Bishop-Gromov type inequality (that is ,roughly speaking, a converse to the Lévy-Gromov’s isoperimetric inequality and was previously only known for Ricci limit spaces) which might be also of independent interest.
Journal Papers
Month/Season:
Summer
Year:
2016