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http://dx.doi.org/10.4134/BKMS.b190913

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)
Publication Information
Bulletin of the Korean Mathematical Society / v.57, no.5, 2020 , pp. 1241-1249 More about this Journal
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 sΩ(𝜂j) tends to 1 or the Fridman invariant hΩ(𝜂j) tends to 0 for some sequence {𝜂j} ⊂ Ω converging to ξ0, then this point must be strongly pseudoconvex.
Keywords
Finite type domains; Fridman invariant; holomorphic mappings; squeezing function;
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