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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


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.


April 7
4:00 pm - 6:00 pm KST
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IBS Korea, Republic of


Sungyeon Kim
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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