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Jihun Yum, Characterization of Diederich-Fornaess and Steinness Indices in Cn

March 24 @ 4:00 pm - 6:00 pm KST

B266, IBS Korea, Republic of

       Speaker

Jihun Yum
IBS, Center for Complex Geometry

Let 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

DF(Ω) := supρ { 0 < η < 1 : -(-ρ)η is strictly plurisubharmonic on Ω ∩ U for some neighborhood U of ∂Ω },

S(Ω) := infρ { η > 1 : ρη is strictly plurisubharmonic on c ∩ U for some neighborhood U of ∂Ω },

where ρ is a defining function for Ω.

First, 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.

We 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

    • two indices are invariant under CR-diffeomorphisms,
    • semi-continuity of two indices.

Details

Date:
March 24
Time:
4:00 pm - 6:00 pm KST
Event Category:

Venue

B266
IBS Korea, Republic of

Organizer

Sungyeon Kim

Instructors

IBS 이산수학그룹 Discrete Mathematics Group
기초과학연구원 복소기하학연구단
대전 유성구 엑스포로 55 (우) 34126
IBS Center for Complex Geometry
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
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