Guenancia, Henri; Paun, Mihai Conic singularities metrics with prescribed Ricci curvature: general cone angles along normal crossing divisors. (English) Zbl 1344.53053 J. Differ. Geom. 103, No. 1, 15-57 (2016). Let \((X, D)\) be a log smooth klt pair, i.e., \(X\) is a compact Kähler manifold and \(D\) is an \(\mathbb R\)-divisor with simple normal crossing support. A natural question to ask in this setting is whether one can find a Kähler-Einstein metric on \(X\setminus \operatorname{Supp}(D)\) having conic singularities along \(D\). Such a metric will be reffered to as a conic Kähler-Einstein metric.This very interesting paper provides a complete (positive) answer to this question (Theorem A) and also derives finer regularity estimates for this type of metric by proving a conic analogue of the Evans-Krylov theorem for complex Monge-Ampère equations (Theorem B). Reviewer: Constantin Călin (Iaşi) Cited in 1 ReviewCited in 62 Documents MSC: 53C55 Global differential geometry of Hermitian and Kählerian manifolds 32Q20 Kähler-Einstein manifolds Keywords:conic singularities metric; prescribed Ricci curvature; general cone angles along normal crossing divisors PDFBibTeX XMLCite \textit{H. Guenancia} and \textit{M. Paun}, J. Differ. Geom. 103, No. 1, 15--57 (2016; Zbl 1344.53053) Full Text: DOI arXiv Euclid