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Sharply estimating hyperbolic capacities

Xiaoshang Jin, Jie Xiao

Abstract

This paper is devoted to establishing four types of sharp capacitary inequalities within the hyperbolic space as detailed in Theorems 2.1-3.1-4.1-5.1.

Sharply estimating hyperbolic capacities

Abstract

This paper is devoted to establishing four types of sharp capacitary inequalities within the hyperbolic space as detailed in Theorems 2.1-3.1-4.1-5.1.

Paper Structure

This paper contains 5 sections, 4 theorems, 137 equations.

Table of Contents

  1. Hyperbolic capacities of general condensers
  2. Sharp capacitary inequalities for smooth condensers
  3. Sharp capacitary inequalities for punctured condensers
  4. Sharp capacitary inequalities for smooth compact domains
  5. Sharp capacitary inequalities for smooth horospherical convex domains

Key Result

Theorem 2.1

Suppose that Then

Theorems & Definitions (8)

  • Theorem 2.1
  • proof
  • Theorem 3.1
  • proof
  • Theorem 4.1
  • proof
  • Theorem 5.1
  • proof