On the structure of RCD spaces with upper curvature bounds

Vitali Kapovitch; Martin Kell; Christian Ketterer

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arXiv · 1908.07036

On the structure of RCD spaces with upper curvature bounds

Vitali Kapovitch·Martin Kell·Christian Ketterer

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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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Vitali Kapovitch, Martin Kell, Christian Ketterer. 2019-08-19. On the structure of RCD spaces with upper curvature bounds. https://arxiv.org/abs/1908.07036

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