A solution of an L2 extension problem with an optimal estimate and applications

• 成果类型: Article
• 署名作者: Guan, Qi'an; Zhou, Xiangyu
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2015.181.3.6
• 发表日期: 2015
• 页码: 1139-1208
• 关键词: ohsawa-takegoshi; holomorphic-functions; bergman-kernel; THEOREM; conjecture; Invariance

摘要

In this paper, we prove an L-2 extension theorem with an optimal estimate in a precise way, which implies optimal estimate versions of various well-known L-2 extension theorems. As applications, we give proofs of a conjecture of Suita on the equality condition in Suita's conjecture, the so-called L-conjecture, and the extended Suita conjecture. As other applications, we give affirmative answer to a question by Ohsawa about limiting case for the extension operators between the weighted Bergman spaces, and we present a relation of our result to Berndtsson's important result on log-plurisubharmonicity of the Bergman kernel.