2022/04/20 by Vitali Kapovitch, Martin Kell, Christian Ketterer +1 · 4 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Algorithm #Boundary (topology) #Bounded function #Combinatorics #Computer science #Curvature #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Manifold (fluid mechanics) #Mathematical analysis #Mathematics #Metric (unit) #Metric space #Space (punctuation) #Submanifold
paper · pdf · doi:10.1007/s00209-022-03015-6
published in Mathematische Zeitschrift 301(4), 3469-3502 (Springer Science+Business Media)
openalex publication_date 2022/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
Abstract We develop a structure theory for \mathrm RCD <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>RCD</mml:mi> </mml:math> 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 \mathrm DC <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>DC</mml:mi> </mml:math> coordinates and the distance is induced by a continuous \mathrm BV <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>BV</mml:mi> </mml:math> Riemannian metric.