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<p>In this paper, we survey the recent progress combining with our results on the geometric function theory of several complex variables in the past two decades. It contains some subclasses of biholomorphic mappings; the growth, covering and distortion theorems for some subclasses of biholomorphic mappings; decomposition theorems for quasi-convex mappings; the estimates of homogeneous expansions for quasi-convex mappings; the Schwarz lemmas and rigidity properties at the boundary for holomorphic self-mappings on some domains. We also propose some open problems in this realm.</p>

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Advances and Further Problems on the Geometric Function Theory of Several Complex Variables

  • 期刊论文

  • 发表日期：

    2025年12月4日

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  • Taishun Liu,
  • Xiaomin Tang,
  • Jianfei Wang

摘要

In this paper, we survey the recent progress combining with our results on the geometric function theory of several complex variables in the past two decades. It contains some subclasses of biholomorphic mappings; the growth, covering and distortion theorems for some subclasses of biholomorphic mappings; decomposition theorems for quasi-convex mappings; the estimates of homogeneous expansions for quasi-convex mappings; the Schwarz lemmas and rigidity properties at the boundary for holomorphic self-mappings on some domains. We also propose some open problems in this realm.