Boundary behavior of the squeezing function near a global extreme point

Thu, Ninh Van; Son, Nguyen Thi Kim; Tiep, Chu Van

doi:10.1080/17476933.2021.1991330

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Proofs Of Theorem 12 and Theorem 131

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2022

2024

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Cited by 2 publications

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“…, q n´1 λ 1{2m n´1 , 0 ¯P D P,r X tz n " 0u, where λ " 1 ´|a| 2 and D P,r X tz n " 0u Ť D P X tz n " 0u. Therefore, by Lemma 2.1 in [NNC21] and again by the invariance of the squeezing function under biholomorphisms, we conclude that σ Ω pqq " σ ψ ´1 a pΩq pψ ´1 a pqqq ą δ{d ą 0, @ q P E r X Bp0; ǫ 0 q, where d denotes the diameter of D P and δ :" distpZ ρ pP q, Z 1 pP qq{2 with Z ρ pP q " tz 1 P C n´1 : P pz 1 q " ru.…”

Section: Proofs Of Theorem 12 and Theorem 13mentioning

confidence: 80%

On the boundary behaviour of the squeezing function near linearly convex boundary points

Thu¹,

Hương²,

Dieu³

2022

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The purpose of this article is twofold. The first aim is to prove that if there exist a sequence tϕ j u Ă AutpΩq and a P Ω such that lim jÑ8 ϕ j paq " ξ 0 and lim jÑ8 σ Ω pϕ j paqq " 1, where ξ 0 is a linearly convex boundary point of finite type, then ξ 0 must be strongly pseudoconvex. Then, the second aim is to investigate the boundary behaviour of the squeezing function of a general ellipsoid.

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Section: Proofs Of Theorem 12 and Theorem 13mentioning

confidence: 80%