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DTSTART;TZID=Asia/Seoul:20210324T160000
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SUMMARY:Jihun Yum\, Characterization of Diederich-Fornaess and Steinness Indices in Cn
DESCRIPTION:     Speaker\n\n\nJihun Yum\nIBS\, Center for Complex Geometry\n\n\n\n\n\n\nLet Ω be a bounded pseudoconvex domain in Cn 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. \nFirst\, we see basic properties and known results about the Diederich-Fornaess and Steinness indices. Also\, we see the relation between two indices on a 1-parameter family of domains in C2\, called worm domains\, constructed by Diederich and Fornaess. \n\nWe characterize the Diederich-Fornaess and Steinness indices in terms of a special 1-form\, which we call D’Angelo 1-form. These formulas are the most important in this talk. After giving a sketch of the proof\, we show many applications and corollaries of the formulas. Especially\, we prove that \n\n\n\ntwo indices are invariant under CR-diffeomorphisms\,\nsemi-continuity of two indices.
URL:https://ccg.ibs.re.kr/event/2021-03-24/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Several Complex Variables Seminar
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