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A Criterion for quasi normality in $\mathbb{C}^n$

Gopal Datt, Sanjay Kumar

Abstract

In this article, we give a Zalcman type renormalization result for the quasinormality of a family of holomorphic functions on a domain in $\mathbb{C}^n$ that takes values in a complete complex Hermitian manifold.

A Criterion for quasi normality in $\mathbb{C}^n$

Abstract

In this article, we give a Zalcman type renormalization result for the quasinormality of a family of holomorphic functions on a domain in that takes values in a complete complex Hermitian manifold.

Paper Structure

This paper contains 3 sections, 8 theorems, 23 equations.

Table of Contents

  1. Introduction
  2. Preliminary Definitions and Main Results
  3. Proof of Main Result

Key Result

Theorem 2.8

AladAK Let $\Omega \subseteq \mathbb{C}^n$ be a hyperbolic domain. Let $M$ be a complete complex Hermitian manifold of dimension $k$ with metric $E_M.$ Let $\mathcal{F}=\{f_{\alpha}\}_{\alpha\in A}\subseteq \emph{Hol}(\Omega, M).$ If the family $\mathcal{F}=\{f_{\alpha}\}_{\alpha\in A}$ is a normal

Theorems & Definitions (28)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Definition 2.4
  • Definition 2.5
  • Definition 2.6
  • Definition 2.7
  • Theorem 2.8
  • Theorem 2.9
  • Theorem 2.10
  • ...and 18 more