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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

Sungyeon Kim