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Corrigendum to "On the heterogeneous distortion inequality"

Ilmari Kangasniemi, Jani Onninen

Abstract

We correct an error in [I. Kangasniemi, and J. Onninen, On the heterogeneous distortion inequality. Math. Ann. 384 (2022), no. 3-4, 1275-1308.]

Corrigendum to "On the heterogeneous distortion inequality"

Abstract

We correct an error in [I. Kangasniemi, and J. Onninen, On the heterogeneous distortion inequality. Math. Ann. 384 (2022), no. 3-4, 1275-1308.]
Paper Structure (1 section, 3 theorems, 39 equations, 1 figure)

This paper contains 1 section, 3 theorems, 39 equations, 1 figure.

Table of Contents

  1. The corrected proof

Key Result

Lemma 7.2

Suppose that a mapping $h \colon \mathbb{R}^n \to \mathbb{R} \times \mathbb{S}^{n-1}$ is continuous and non-constant, and that $h \in W^{1,n}_\mathrm{loc}(\mathbb{R}^n, \mathbb{R} \times \mathbb{S}^{n-1})$ with $\left| Dh \right| \in L^n(\mathbb{R}^n)$. If $h$ satisfies the distortion inequality eq:

Figures (1)

  • Figure 1: The points $x_i$ and the balls $B_i$ and $B_i'$.

Theorems & Definitions (7)

  • Remark 1.1
  • Lemma 7.2: revised
  • Lemma 7.3
  • proof
  • proof : Proof of the revised Lemma \ref{['prop:log_integrability']}
  • Theorem 1.3
  • proof