The paper “A solution of an L² extension problem with optimal estimate and applications " authored by CAS Academician Prof.ZHOU Xiangyu, from AMSS and his student Doctor GUAN Qian was accepted on Annals of Mathematics.

In the paper, they prove an L² extension theorem with optimal estimate in a precise way, which implies optimal estimate versions of various well-known L ² extension theorems. As applications, they 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, they give affirmative answer to a question by Ohsawa about limiting case for the extension operators between the weighted Bergman spaces, and they present a relation of our result to Berndtsson’s important result on log-plurisubharmonicity of Bergman kernel.

Prof.ZHOU solved the extended future tube conjecture which was posed in 1950's and widely studied by the schools of Bogolyubov’s and Wightman’s when they studied quantum field theory and Hilbert's 6th problem, and was listed as an open problem in the “Encyclopedia of Mathematics”. He proved the Sergeev conjecture about the characterization of a matrix Reinhardt domain being a domain of holomorphy. He found in a unified way a criteria of envelope of holomorphy of certain invariant domains to be univalent. He also initiated a method to approach an L2 extension problem with optimal estimate and solved the problem with various applications (together with his student).

Prof. ZHOU Xiangyu got his Doctor of Science Degree  at Steklov Mathematical Institute (Moscow) in 1999. He was honored with the Second Class Prize of National Natural Science Award in 2004. Besides, he was the invited speaker of International Congress of Mathematicians in 2002, and the invited keynote speaker of Abel Symposium in 2013.

The Annals of Mathematics which is recognized as the top journal in mathematics is published bimonthly by the Department of Mathematics at Princeton University with the cooperation of the Institute for Advanced Study.