A solution of an $L^2$ extension problem with optimal estimate and applications

Abstract

In this paper, we prove an $L^2$ extension theorem with 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 Bergman kernel.

59 pages, 0 figure

References in corpus (3)

• Bergman kernels and subadjunction
• A Bergman kernel proof of the Kawamata subadjunction theorem
• Some results related to group actions in several complex variables

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• An extension theorem of Ohsawa-Takegoshi type for sections of a vector bundle
• Potential Theoretic Hyperbolicity and ${\mathbf{L}}^2$ extension. Part I: Stein manifolds