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May 2016 Conic singularities metrics with prescribed Ricci curvature: General cone angles along normal crossing divisors
Henri Guenancia, Mihai Paun
J. Differential Geom. 103(1): 15-57 (May 2016). DOI: 10.4310/jdg/1460463562

Abstract

Let $X$ be a non-singular compact Kähler manifold, endowed with an effective divisor $D=\sum{(1-\beta_k) Y_k}$ having simple normal crossing support, and satisfying $\beta_k \in (0, 1)$. The natural objects one has to consider in order to explore the differential-geometric properties of the pair $(X,D)$ are the so-called metrics with conic singularities. In this article, we complete our earlier work concerning the Monge-Ampère equations on $(X,D)$ by establishing Laplacian and $\mathscr{C}^{2,\alpha,\beta}$ estimates for the solution of these equations regardless of the size of the coefficients $0 \lt \beta_k \lt 1$. In particular, we obtain a general theorem concerning the existence and regularity of Kähler–Einstein metrics with conic singularities along a normal crossing divisor.

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Henri Guenancia. Mihai Paun. "Conic singularities metrics with prescribed Ricci curvature: General cone angles along normal crossing divisors." J. Differential Geom. 103 (1) 15 - 57, May 2016. https://doi.org/10.4310/jdg/1460463562

Information

Published: May 2016
First available in Project Euclid: 12 April 2016

zbMATH: 1344.53053
MathSciNet: MR3488129
Digital Object Identifier: 10.4310/jdg/1460463562

Rights: Copyright © 2016 Lehigh University

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Vol.103 • No. 1 • May 2016
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