Kahler-Einstein metrics with edge singularities

• 成果类型: Article
• 署名作者: Jeffres, Thalia; Mazzeo, Rafe; Rubinstein, Yanir A.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2016.183.1.3
• 发表日期: 2016
• 页码: 95-176
• 关键词: monge-ampere equations; RICCI CURVATURE; elliptic theory; MANIFOLDS; inequalities; asymptotics; uniqueness; STABILITY; LIMITS; SPACE

摘要

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.