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

April 7 @ 4:00 pm - 6:00 pm KST

B266, IBS Korea, Republic of

Speaker

Jihun Yum
IBS, Center for Complex Geometry

Let 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

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.

In 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.

Details

Date:
April 7
Time:
4:00 pm - 6:00 pm KST
Event Category:

Venue

B266
IBS Korea, Republic of

Sungyeon Kim