Kähler--Einstein metrics with edge singularities

2011/05/31 by Thalia Jeffres, T. Jeffres, Rafe Mazzeo +2 · 1 citation
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory #math.AP #math.DG #msc:32Q20

paper · pdf · doi:10.4007/annals.2016.183.1.3

published as Annals of Math. 183 (2016), 95-176 · with an appendix by Chi Li and Yanir A. Rubinstein. Accepted by Annals of Math

arxiv created 2015/08/08 · openalex publication_date 2015/11/20 · arxiv updated 2015/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

This article considers the existence and regularity of Kahler Einstein metrics on a compact Kahler manifold M with edge singularities with cone angle 2 pi beta along a smooth divisor D. We prove existence of such metrics with negative, zero and some positive cases for all cone angles 2 pi beta <= 2 pi. The results in the positive case parallel those in the smooth case. We also establish that solutions of this problem are polyhomogeneous, i.e., have a complete asymptotic expansion with smooth coefficients along D for all 2 pi beta < 2 pi.

Citations

• Elliptic Partial Differential Equations of Second Order
• Harmonic Mappings of Riemannian Manifolds
• Some discretizations of geometric evolution equations and the Ricci iteration on the space of Kähler metrics
• On the ricci curvature of a compact kähler manifold and the complex monge‐ampére equation, I
• Complete Kahler Manifolds with Zero Ricci Curvature. I
• Einstein Manifolds

Cited by

• Rafe Mazzeo [wikipedia]