2017/12/07 by Vitali Kapovitch, Christian Ketterer, C. Ketterer +2 · 1 citation
Mathematics · #Advanced Operator Algebra Research #Geometric Analysis and Curvature Flows #Homotopy and Cohomology in Algebraic Topology #math.DG #math.MG #msc:53C20 #msc:53C21
paper · pdf · doi:10.48550/arxiv.1712.02839
We add a new section where we prove a new theorem that if a $CD(K,n)$ space with finite $n$ has curvature bounded above then it is infinitesimally Hilbertian. Using this we remove the infinitesimal Hilbertianness assumption from the main theorem. Minor corrections, additional references
arxiv created 2018/01/20 · arxiv updated 2018/01/23
We show that if a noncollapsed CD(K,n) space X with n≥ 2 has curvature bounded above by κ in the sense of Alexandrov then K≤ (n-1)κ and X is an Alexandrov space of curvature bounded below by K-κ(n-2). We also show that if a CD(K,n) space Y with finite n has curvature bounded above then it is infinitesimally Hilbertian.