A note on the boundary behaviour of the squeezing function and Fridman invariant

2019/07/10 by Ninh, Van Thu, Mai, Anh Duc, Nguyen, Thi Lan Huong +1
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1907.04528

Abstract

Let Ω be a domain in \mathbb 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_Ω(η_j) tends to 1 or the Fridman invariant h_Ω(η_j) tends to 0 for some sequence \η_j\⊂ Ω converging to ξ₀, then this point must be strongly pseudoconvex.

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