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

2013/10/27 by Qi’an Guan, Xiangyu Zhou, Guan, Qi'an +1 · 9 citations
Mathematics · #Geometry and complex manifolds #Holomorphic and Operator Theory #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.1310.7169

Abstract

In this paper, we prove an L² extension theorem with optimal estimate in a precise way, which implies optimal estimate versions of various well-known L² 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 Bergman kernel.

Citations

• Bergman kernels and the pseudoeffectivity of relative canonical bundles

Cited by

• Siu's curvature positivity and L² extension theorems for (p,q)-forms
• An extension theorem of Ohsawa-Takegoshi type for sections of a vector bundle
• On the p-Bergman kernel with respect to a functional ξ
• Positivity and L² Extension
• On the Suita conjecture for some convex ellipsoids in \mathbb C²
• Estimates for the Bergman Kernel and the Multidimensional Suita Conjecture
• An extension theorem in terms of adjoint ideal sheaves
• An optimal L² extension for continuous L²-optimal Hermitian metrics
• An Ohsawa-Takegoshi-type L² extension for upper semi-continuous L²-optimal functions

Related

• A simplified proof of optimal L²-extension theorem and extensions from non-reduced subvarieties
• On sharper estimates of Ohsawa-Takegoshi L²-extension theorem
• Optimal L²-extensions on tube domains and a simple proof of Prékopa's theorem
• Sharper estimates of Ohsawa--Takegoshi L²-extension theorem in higher dimensional case
• Weighted L² estimates with applications to L^p problems