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On the structure of RCD spaces with upper curvature bounds (1908.07036v2)
Published 19 Aug 2019 in math.DG and math.MG
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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