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A COMPACTNESS THEOREM FOR SURFACES WITH BOUNDED INTEGRAL CURVATURE

Part of: Global differential geometry

Published online by Cambridge University Press:  10 April 2018

Clément Debin
Clément Debin*
Affiliation:
Institut Fourier, Mathematics, Saint Martin d’Heres, France, 38402 ([email protected])
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Abstract

We prove a compactness theorem for metrics with bounded integral curvature on a fixed closed surface $\unicode[STIX]{x1D6F4}$. As a corollary we obtain a new convergence result for sequences of metrics with conical singularities, where an accumulation of singularities is allowed.

Keywords

differential geometrymetric geometryconical singularitiesAlexandrov surfaces with bounded integral curvaturecompactness theorem

MSC classification

Primary: 53C23: Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 19 , Issue 2 , March 2020 , pp. 597 - 645
Copyright
© Cambridge University Press 2018

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Footnotes

This research is supported by the ERC advanced grant 320939, Geometry and Topology of Open Manifolds (GETOM).

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