The limit spaces of two-dimensional manifolds with uniformly bounded integral curvature

DOI10.1090/S0002-9947-99-02103-0zbMath0942.53027MaRDI QIDQ4235611

Takashi Shioya

Publication date: 22 March 1999

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Gromov-Hausdorff convergencetotal curvaturetriangle comparison\(L^p\)-curvature bound

Mathematics Subject Classification ID

Spaces of embeddings and immersions (58D10) Global Riemannian geometry, including pinching (53C20)

Related Items (6)

On conformal planes of finite area ⋮ Tropical Geometric Compactification of Moduli, I – M g Case ⋮ Comparison geometry referred to warped product models ⋮ Space of minimal discs and its compactification ⋮ Bi-Lipschitz-equivalent Aleksandrov surfaces, II ⋮ A COMPACTNESS THEOREM FOR SURFACES WITH BOUNDED INTEGRAL CURVATURE

Cites Work

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• Collapsing of Riemannian manifolds and eigenvalues of Laplace operator
• A concentration-compactness principle for sequences of Riemannian surfaces.
• Comparison geometry with integral curvature bounds
• Convergence of riemannian manifolds with integral bounds on curvature. I
• Geodesic Parallel Coordinates in the Large
• Total excess on length surfaces

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