A COMPACTNESS THEOREM FOR SURFACES WITH BOUNDED INTEGRAL CURVATURE

DOI10.1017/S1474748018000154zbMath1436.53025arXiv1605.07755OpenAlexW2395158901MaRDI QIDQ5221324

Clément Debin

Publication date: 25 March 2020

Published in: Journal of the Institute of Mathematics of Jussieu (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.07755

zbMATH Keywords

conical singularitiesmetric geometrycompactness theoremAlexandrov surfaces with bounded integral curvature

Mathematics Subject Classification ID

Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Global surface theory (convex surfaces à la A. D. Aleksandrov) (53C45)

Related Items (4)

Isoperimetric inequalities and geometry of level curves of harmonic functions on smooth and singular surfaces ⋮ Triangulating metric surfaces ⋮ A Pu-Bonnesen inequality ⋮ Geometry and entropies in a fixed conformal class on surfaces

Cites Work

• Convergence and rigidity of manifolds under Ricci curvature bounds
• Lipschitz convergence of Riemannian manifolds
• Geometrische Methoden zur Gewinnung von a-priori-Schranken für harmonische Abbildungen
• A concentration-compactness principle for sequences of Riemannian surfaces.
• \(C^ \alpha\)-compactness for manifolds with Ricci curvature and injectivity radius bounded below
• Some regularity theorems in riemannian geometry
• The limit spaces of two-dimensional manifolds with uniformly bounded integral curvature
• A convergence theorem for Riemannian manifolds and some applications
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