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Annals of Global Analysis and Geometry

, Volume 52, Issue 4, pp 457–464 | Cite as

Kähler metrics with cone singularities along a divisor of bounded Ricci curvature

Article
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Abstract

Let D be a smooth divisor in a compact complex manifold X and let \(\beta \in (0,1)\). We use the liner theory developed by Donaldson (Essays in Mathematics and Its Applications, Springer, Berlin, pp 49–79, 2012) to show that in any positive co-homology class on X there is a Kähler metric with cone angle \(2\pi \beta \) along D which has bounded Ricci curvature. We use this result together with the Aubin–Yau continuity method to give an alternative proof of a well-known existence theorem for Kähler–Einstein metrics with cone singularities.

Keywords

Kähler–Einstein metrics Complex Monge–Ampère equation Kähler metrics with cone singularities 

Notes

Acknowledgements

This article contains material from the author’s PhD Thesis at Imperial College, founded by the European Research Council Grants 247331 and defended in December 2015. I wish to thank my supervisor, Simon Donaldson, for his encouragement and support.

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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Universidad Nacional de San LuisSan LuisArgentina

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