Zhou Xiangyu solved the long-standing conjecture that the extended future light pipe domain is holomorphic domain. This conjecture was put forward by Bogolyubov and Wightman school from the study of quantum field theory and Hilbert's sixth problem, and it was listed as an unsolved problem in the mathematical encyclopedia. Zhou Xiangyu's work was written into Mathematical Events in the Twentieth Century and Development of Mathematics: 1950-2000 by the Russian Academy of Sciences and the Royal Swedish Academy of Sciences respectively. It is considered as "one of the highlights of the development of mathematics", and takes this as an example to illustrate "how mathematics helps physics acquire new knowledge hidden in axioms".
Zhou Xiangyu gave the criterion that the holomorphic packet of the orbit-connected general compact Lie group invariant domain is univalent, which solved the basic problem of univalence of holomorphic packets. The conjecture that Reinhardt domain of matrix is characterized as holomorphic domain is proved. This work is considered to be "the main result of the difficulty in univalence of holomorphic packages" in the American Mathematical Review.
Xiang Xiangyu and others cooperated to solve the optimal constant problem in L- extension theorem, and solved the famous Suita conjecture put forward as an inference forty years ago. Previously, many mathematicians, such as Xiao (academician of American Academy of Sciences), De Mairi (academician of French Academy of Sciences), Berndt Song (academician of Royal Academy of Sciences) and osawa, have studied this problem and got some good constant estimates, but they have not been solved.
Zhou Xiangyu was also invited to give a keynote speech at the Abel conference held in Norway in June 20 13. World-leading experts in complex geometry, complex analysis and complex dynamic systems were invited to attend the conference.
He is now the editorial board of advances in mathematics, the editorial board of China Science and the executive director of the Chinese Mathematical Society. He has won the National Science Fund for Distinguished Young Scholars (1998), Qiushi Outstanding Young Scholars Award (1998), the first prize of Natural Science Award of China Academy of Sciences (1999), the 8th Chen Shengshen Mathematics Award (chinese mathematical society) (200 1) and the National Natural Science Award. He was awarded the Russian National Doctor of Science (1998) by the stech Loff Institute of Mathematics of the Russian Academy of Sciences, an internationally renowned mathematics center, and gave a 45-minute invitation report at the International Congress of Mathematicians in 2002. "Russian mathematics. Investigation published a special article in 2003 to introduce the 2002 International Congress of Mathematicians. When introducing this 45-minute report, Zhou Xiangyu's report was rated as one of the six selected reports.