On the structure of spaces with upper curvature bounds
V Kapovitch, M Kell, C Ketterer - Mathematische Zeitschrift, 2022 - Springer
V Kapovitch, M Kell, C Ketterer
Mathematische Zeitschrift, 2022•SpringerWe 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.
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.
Abstract
We develop a structure theory for 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 coordinates and the distance is induced by a continuous Riemannian metric.
Springer
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