On the structure of RCD spaces with upper curvature bounds
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
- Location
-
Deutsche Nationalbibliothek Frankfurt am Main
- Extent
-
Online-Ressource
- Language
-
Englisch
- Notes
-
Mathematische Zeitschrift. - 301, 4 (2022) , 3469-3502, ISSN: 1432-1823
- Event
-
Veröffentlichung
- (where)
-
Freiburg
- (who)
-
Universität
- (when)
-
2024
- Creator
- DOI
-
10.1007/s00209-022-03015-6
- URN
-
urn:nbn:de:bsz:25-freidok-2448541
- Rights
-
Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
- 14.08.2025, 11:03 AM CEST
Data provider
This object is provided by:
Deutsche Nationalbibliothek. If you have any questions about the object, please contact the data provider.
Deutsche Nationalbibliothek. If you have any questions about the object, please contact the data provider.
Associated
- Kapovitch, Vitali
- Kell, Martin
- Ketterer, Christian Eugen Michael
- Universität
Time of origin
- 2024
Other Objects (12)
Weakly Noncollapsed RCD Spaces with Upper Curvature Bounds
On the structure of $$\mathrm RCD}$$ RCD spaces with upper curvature bounds
Orbifolds and Manifold Quotients with Upper Curvature Bounds
Metric measure spaces satisfying Ricci curvature lower bounds 4
Metric measure spaces satisfying Ricci curvature lower bounds 1
Metric measure spaces satisfying Ricci curvature lower bounds 2
Metric measure spaces satisfying Ricci curvature lower bounds 3
Curvature bounds and heat kernels: discrete versus continuous spaces
Geometry of spaces with a synthetic lower curvature bound
Comparison properties of diffusion semigroups on spaces with lower curvature bounds
Comparison properties of diffusion semigroups on spaces with lower curvature bounds
Curvature bounds on length-minimizing discs
Weakly Noncollapsed RCD Spaces with Upper Curvature Bounds
On the structure of $$\mathrm RCD}$$ RCD spaces with upper curvature bounds
Orbifolds and Manifold Quotients with Upper Curvature Bounds
Metric measure spaces satisfying Ricci curvature lower bounds 4
Metric measure spaces satisfying Ricci curvature lower bounds 1
Metric measure spaces satisfying Ricci curvature lower bounds 2
Metric measure spaces satisfying Ricci curvature lower bounds 3
Curvature bounds and heat kernels: discrete versus continuous spaces
Geometry of spaces with a synthetic lower curvature bound
Comparison properties of diffusion semigroups on spaces with lower curvature bounds
Comparison properties of diffusion semigroups on spaces with lower curvature bounds
Curvature bounds on length-minimizing discs
Weakly Noncollapsed RCD Spaces with Upper Curvature Bounds
On the structure of $$\mathrm RCD}$$ RCD spaces with upper curvature bounds
Orbifolds and Manifold Quotients with Upper Curvature Bounds
Metric measure spaces satisfying Ricci curvature lower bounds 4
Metric measure spaces satisfying Ricci curvature lower bounds 1
Metric measure spaces satisfying Ricci curvature lower bounds 2
Metric measure spaces satisfying Ricci curvature lower bounds 3
Curvature bounds and heat kernels: discrete versus continuous spaces
Geometry of spaces with a synthetic lower curvature bound
Comparison properties of diffusion semigroups on spaces with lower curvature bounds
Comparison properties of diffusion semigroups on spaces with lower curvature bounds