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arXiv · 1612.01866

K\"ahler metrics with cone singularities along a divisor of bounded Ricci curvature

Martin de Borbon
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Abstract

Let $D$ be a smooth divisor in a compact complex manifold $X$ and let $\beta \in (0,1)$. We show that in any positive co-homology class on $X$ there is a K\"ahler 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 Kahler-Einstein metrics with cone singularities.

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Martin de Borbon. 2016-12-06. K\"ahler metrics with cone singularities along a divisor of bounded Ricci curvature. https://doi.org/10.1007/s10455-017-9565-1

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