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

Qi'an Guan; Xiangyu Zhou

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arXiv · 1310.7169

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

Qi'an Guan·Xiangyu Zhou

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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.

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Qi'an Guan, Xiangyu Zhou. 2014-01-31. A solution of an $L^{2}$ extension problem with optimal estimate and applications. https://arxiv.org/abs/1310.7169

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