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Register a new userEstimates for the squeezing function near strictly pseudoconvex boundary points with applications
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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.
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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.
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 investigate regularity properties of the $overline{partial}$-equation on domains in a complex euclidean space that depend on a parameter. Both the interior regularity and the regularity in the parameter are obtained for a continuous family of pseudoconvex domains. The boundary regularity and the regularity in the parameter are also obtained for smoothly bounded strongly pseudoconvex domains.
We construct a complete proper holomorphic embedding from any strictly pseudoconvex domain with $mathcal{C}^2$-boundary in $mathbb{C}^n$ into the unit ball of $mathbb{C}^N$, for $N$ large enough, thereby answering a question of Alarcon and Forstneric.
In this paper, we generalize a recent work of Liu et al. from the open unit ball $mathbb B^n$ to more general bounded strongly pseudoconvex domains with $C^2$ boundary. It turns out that part of the main result in this paper is in some certain sense just a part of results in a work of Bracci and Zaitsev. However, the proofs are significantly different: the argument in this paper involves a simple growth estimate for the Caratheodory metric near the boundary of $C^2$ domains and the well-known Grahams estimate on the boundary behavior of the Caratheodory metric on strongly pseudoconvex domains, while Bracci and Zaitsev use other arguments.
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