Geodesic
A solution of an $L^{2}$ extension problem with an optimal estimate and applications
Qi'an Guan1 ; Xiangyu Zhou2
1 Beijing International Center for Mathematical Research, and School of Mathematical Sciences, Peking University, Beijing 100871, China
2 Institute of Mathematics, AMSS, and Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing 100190, China
Annals of mathematics, Tome 181 (2015) no. 3, pp. 1139-1208.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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.
DOI : 10.4007/annals.2015.181.3.6

Qi'an Guan 1 ; Xiangyu Zhou 2

1 Beijing International Center for Mathematical Research, and School of Mathematical Sciences, Peking University, Beijing 100871, China
2 Institute of Mathematics, AMSS, and Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing 100190, China 
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Qi'an Guan; Xiangyu Zhou. A solution of an $L^{2}$ extension problem with an optimal estimate and applications. Annals of mathematics, Tome 181 (2015) no. 3, pp. 1139-1208. doi : 10.4007/annals.2015.181.3.6. http://geodesic.mathdoc.fr/articles/10.4007/annals.2015.181.3.6/

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