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DTSTART;TZID=Asia/Seoul:20210407T160000
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SUMMARY:Jihun Yum\,  Characterization of Diederich-Fornaess and Steinness Indices in Complex Manifolds
DESCRIPTION:     Speaker\n\n\nJihun Yum\nIBS\, Center for Complex Geometry\n\n\n\n\n\n\nLet Ω be a relatively compact pseudoconvex domain in a complex manifold X with smooth boundary ∂Ω. The Diederich-Fornaess index and the Steinness index of Ω are defined by \nDF(Ω) := supρ { 0 < η < 1 : -(-ρ)η is strictly plurisubharmonic on Ω ∩ U for some neighborhood U of ∂Ω }\, \nS(Ω) := infρ { η > 1 : ρη is strictly plurisubharmonic on Ωc ∩ U for some neighborhood U of ∂Ω }\, \nwhere ρ is a defining function for Ω. \nIn the previous talk\, we have seen that two indices are completely characterized by D’Angelo 1-form when the ambient space is X = Cn. In this talk\, we generalize the formulas for a relatively compact pseudoconvex domains in a (general) complex manifold X. Since the formulas do not hold anymore in general\, unfortunately\, we introduce 4 kinds of each of the Diederich-Fornaess and Steinness indices. Then we give some non-degeneracy conditions for these indices agree. Also\, we exam the geometric meaning of the D’Angelo 1-form when the boundary ∂Ω is Levi-flat.
URL:https://ccg.ibs.re.kr/event/2021-04-07/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Several Complex Variables Seminar
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