# A NOTE ON THE BOUNDARY BEHAVIOUR OF THE SQUEEZING FUNCTION AND FRIDMAN INVARIANT

• Kim, Hyeseon (Research Institute of Mathematics Seoul National University) ;
• Mai, Anh Duc (Faculty of Mathematics Physics and Informatics Tay Bac University) ;
• Nguyen, Thi Lan Huong (Department of Mathematics Hanoi University of Mining and Geology) ;
• Ninh, Van Thu (Department of Mathematics Vietnam National University at Hanoi)
• Received : 2019.10.14
• Accepted : 2020.05.14
• Published : 2020.09.30

#### Abstract

Let Ω be a domain in ℂn. Suppose that ∂Ω is smooth pseudoconvex of D'Angelo finite type near a boundary point ξ0 ∈ ∂Ω and the Levi form has corank at most 1 at ξ0. Our goal is to show that if the squeezing function s(𝜂j) tends to 1 or the Fridman invariant h(𝜂j) tends to 0 for some sequence {𝜂j} ⊂ Ω converging to ξ0, then this point must be strongly pseudoconvex.

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