Calabi flow, geodesic rays, and uniqueness of constant scalar curvature Kahler metrics

• 成果类型: Article
• 署名作者: Chen, Xiuxiong; Sun, Song
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2014.180.2.1
• 发表日期: 2014
• 页码: 407-454
• 关键词: projective embeddings; symplectic-manifolds; extremal metrics; mabuchi energy; moduli space; STABILITY; asymptotics; invariant; geometry; blowups

摘要

We prove that constant scalar curvature Kahler metric adjacent to a fixed Kahler class is unique up to isomorphism. The proof is based on the study of a fourth order evolution equation, namely, the Calabi flow, from a new geometric perspective, and on the geometry of the space of Kahler metrics.