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Jihun Yum, Characterization of DiederichFornaess and Steinness Indices in C^{n}
March 24 @ 4:00 pm  6:00 pm KST
Let Ω be a bounded pseudoconvex domain in C^{n} with smooth boundary ∂Ω. The DiederichFornaess index and the Steinness index of Ω are defined by
DF(Ω) := sup_{ρ} { 0 < η < 1 : (ρ)^{η} is strictly plurisubharmonic on Ω ∩ U for some neighborhood U of ∂Ω },
S(Ω) := inf_{ρ} { η > 1 : ρ^{η} is strictly plurisubharmonic on Ω^{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 DiederichFornaess and Steinness indices. Also, we see the relation between two indices on a 1parameter family of domains in C^{2}, called worm domains, constructed by Diederich and Fornaess.
We characterize the DiederichFornaess and Steinness indices in terms of a special 1form, which we call D’Angelo 1form. 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 CRdiffeomorphisms,
 semicontinuity of two indices.