Kähler metrics with cone singularities along a divisor of bounded Ricci curvature
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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.
KeywordsKähler–Einstein metrics Complex Monge–Ampère equation Kähler metrics with cone singularities
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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