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Alexander-Taylor's inequality for capacities in complex Sobolev spaces

Ngoc Cuong Nguyen, Do Duc Thai

Abstract

We prove a sharp inequality between the Alexander-Taylor capacity and the functional capacity in a complex Sobolev space on a compact Kähler manifold. The latter space and capacity were introduced by Dinh, Sibony and Vigny.

Alexander-Taylor's inequality for capacities in complex Sobolev spaces

Abstract

We prove a sharp inequality between the Alexander-Taylor capacity and the functional capacity in a complex Sobolev space on a compact Kähler manifold. The latter space and capacity were introduced by Dinh, Sibony and Vigny.
Paper Structure (6 sections, 14 theorems, 85 equations)

This paper contains 6 sections, 14 theorems, 85 equations.

Table of Contents

  1. Introduction
  2. A functional capacity in complex Sobolev spaces
  3. Local and global definitions of capacities
  4. Quasi-continuous representative
  5. The Alexander-Taylor capacity
  6. Comparison of capacities

Key Result

Theorem 1.1

There exists a constant $A>0$ such that for every compact subset $K\subset X$,

Theorems & Definitions (31)

  • Theorem 1.1
  • Corollary 1.2
  • Definition 2.1: DS
  • Lemma 2.2
  • Proposition 2.3
  • Proposition 2.4
  • Lemma 2.5: outer regularity
  • proof
  • Lemma 2.6
  • Definition 2.7
  • ...and 21 more