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Asymptotic characterizations of strong pseudoconvexity on pseudoconvex domains of finite type in $\mathbb{C}^2$

Jinsong Liu, Xingsi Pu, Lang Wang

Abstract

In this paper, we provide some characterizations of strong pseudoconvexity by the boundary behavior of intrinsic invariants for smoothly bounded pseudoconvex domains of finite type in $\mathbb{C}^2$. As a consequence, if such domain is biholomorphically equivalent to a quotient of the unit ball, then it is strongly pseudoconvex.

Asymptotic characterizations of strong pseudoconvexity on pseudoconvex domains of finite type in $\mathbb{C}^2$

Abstract

In this paper, we provide some characterizations of strong pseudoconvexity by the boundary behavior of intrinsic invariants for smoothly bounded pseudoconvex domains of finite type in . As a consequence, if such domain is biholomorphically equivalent to a quotient of the unit ball, then it is strongly pseudoconvex.
Paper Structure (11 sections, 15 theorems, 86 equations)

This paper contains 11 sections, 15 theorems, 86 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notations
  4. The Invariant Metrics
  5. Holomorphic Sectional Curvature
  6. Squeezing Function
  7. Pseudoconvex domain of finite type in $\mathbb{C}^2$
  8. Scaling Sequence
  9. Stability of Intrinsic Invariants
  10. Quasi-bounded Geometry
  11. Proof of Theorem \ref{['thm1']}

Key Result

Theorem 1.1

Suppose $\Omega\subset\mathbb{C}^n$ is a bounded strongly pseudoconvex domain with $C^2$-smooth boundary, then the following statements hold (1) $\lim\limits_{z\rightarrow\partial\Omega} s_{\Omega}(z)=1$, where $s_{\Omega}(z)$ is the squeezing function of $\Omega$. (2) $\lim\limits_{z\rightarrow\par

Theorems & Definitions (29)

  • Theorem 1.1
  • Theorem 1.2
  • Proposition 1.3
  • Corollary 1.4
  • Remark 2.1
  • Definition 2.2
  • Remark 2.3
  • Remark 2.4
  • Definition 3.1
  • Proposition 3.2: kra
  • ...and 19 more