On the structure of RCD spaces with upper curvature bounds

2019/08/19 by Vitali Kapovitch, Martin Kell, Kapovitch, Vitali +3
Mathematics · #53C20 #53C21 #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG) #math.DG #math.MG #msc:53C20 #msc:53C21

paper · pdf · doi:10.48550/arxiv.1908.07036

paragraph in the introduction after the main theorem added, 30 pages, comments are welcome

arxiv created 2019/09/07 · arxiv updated 2019/09/10

Abstract

We develop a structure theory for RCD spaces with curvature bounded above in Alexandrov sense. In particular, we show that any such space is a topological manifold with boundary whose interior is equal to the set of regular points. Further the set of regular points is a smooth manifold and is geodesically convex. Around regular points there are DC coordinates and the distance is induced by a continuous BV Riemannian metric.

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