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Register a new userBehavior of the squeezing function near h-extendible boundary points
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Authors
Nikolai Nikolov
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It is shown that if the squeezing function tends to one at an h-extendible boundary point of a $mathcal C^infty$-smooth, bounded pseudoconvex domain, then the point is strictly pseudoconvex.
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An extension of the estimates for the squeezing function of strictly pseudoconvex domains obtained recently by J. E. Fornae ss and E. Wold in cite{FW1} is applied to derive a sharp boundary behaviour of invariant metrics and Bergman curvatures.
J. E. Fornaess has posed the question whether the boundary point of smoothly bounded pseudoconvex domain is strictly pseudoconvex, if the asymptotic limit of the squeezing function is 1. The purpose of this paper is to give an affirmative answer when the domain is in C^2 with smooth boundary of finite type in the sense of DAngelo.
We describe the boundary behaviors of the squeezing functions for all bounded convex domains in $mathbb{C}^n$ and bounded domains with a $C^2$ strongly convex boundary point.
In the present article, we define squeezing function corresponding to polydisk and study its properties. We investigate relationship between squeezing fuction and squeezing function corresponding to polydisk.
For a domain $D subset mathbb C^n$, the relationship between the squeezing function and the Fridman invariants is clarified. Furthermore, localization properties of these functions are obtained. As applications, some known results concerning their boundary behavior are extended.
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