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Positive solutions of a critical equation in sub-Finsler geometry

Nicola Garofalo, Paolo Salani

Abstract

We compute a two-parameter family of explicit positive solutions of a critical Yamabe type equation for a nonlinear operator that sits at the intersection of Finsler and sub-Riemannian geometry

Positive solutions of a critical equation in sub-Finsler geometry

Abstract

We compute a two-parameter family of explicit positive solutions of a critical Yamabe type equation for a nonlinear operator that sits at the intersection of Finsler and sub-Riemannian geometry
Paper Structure (3 sections, 9 theorems, 66 equations)

This paper contains 3 sections, 9 theorems, 66 equations.

Table of Contents

  1. Introduction
  2. Proof of Theorem \ref{['T:yam']}
  3. Appendix: Minkowski norms

Key Result

Theorem 1.2

For $\varepsilon>0$ and $\sigma_0\in \mathbb{R}^k$, consider the function Then $K_{\varepsilon,\sigma_0}$ is a positive entire solution of the partial differential equation yamme in $\mathbb{R}^N$.

Theorems & Definitions (15)

  • Remark 1.1
  • Theorem 1.2
  • Lemma 2.1
  • Lemma 2.2
  • Proposition 2.3
  • proof
  • Theorem 2.4
  • Lemma 2.5
  • proof
  • Lemma 2.6
  • ...and 5 more