报告人：Siqi Fu 教授 Rutgers University–Camden
报告题目：Hearing pseudoconvexity in Lipschitz domains with holes via ∂ ̄
时 间：2017年6月20日（星期二）15：00 -16：00
地 点：旗山校区理工北楼601报告厅
主 办：数学与计算机科学学院, 福建省分析数学及应用重点实验室, 数学研究中心
参加对象：相关研究方向老师和研究生
报告摘要：In this talk, we explain how one can determine pseudoconvexity in Lipschitz domains with holes via spectral property of the ∂ ̄-Neumann Laplacian. More precisely, let Ω = Ω\ D where Ωis a bounded domain with connected complement in Cn and D is relatively compact open subset of Ωwith connected complement in Ω. We obtain characterizations of pseudoconvexity of Ωand D through the vanishing or Hausdorff property of the Dolbeaultcohomology groups on various function spaces. In particular, we show that if the boundaries of Ωand D are Lipschitz and C2-smooth respectively, then both Ωand D arepseudoconvex if and only if 0 is not in the spectrum of the ∂-Neumann Laplacian on (0,q)-forms for 1 ≤ q ≤ n − 2 when n ≥ 3; or 0 is not a limit point of the spectrum of the ∂-Neumannn Laplacian on (0, 1)-forms when n = 2. This is a joint work with Christine Laurent-Thi ́ebaut and Mei-Chi Shaw.
专家简介：Siqi Fu，Rutgers University–Camden教授， 1984年获华南师范大学学士学位，1987年获北京大学硕士学位，1994年获Washington University博士学位。
