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On an evolution equation in sub-Finsler geometry

Nicola Garofalo

Abstract

We study the gradient flow of an energy with mixed homogeneity which is at the interface of Finsler and sub-Riemannian geometry

On an evolution equation in sub-Finsler geometry

Abstract

We study the gradient flow of an energy with mixed homogeneity which is at the interface of Finsler and sub-Riemannian geometry
Paper Structure (5 sections, 14 theorems, 144 equations)

This paper contains 5 sections, 14 theorems, 144 equations.

Table of Contents

  1. Introduction
  2. Minkowski norms
  3. Equalities matter
  4. Construction of the heat kernel
  5. The nonlinear heat equation sees the anisotropic Minkowski gauge $\Theta^0$

Key Result

Theorem 1.1

For every $X = (z,\sigma)\in \mathbb{R}^N$ and $t>0$ the function is a solution of the equation pde. Moreover, for every $t>0$ we have

Theorems & Definitions (21)

  • Theorem 1.1
  • Remark 1.2
  • Theorem 1.3
  • Lemma 2.1
  • Proposition 2.2
  • Proposition 2.3
  • Proposition 2.4
  • Remark 2.5
  • Lemma 2.6
  • proof
  • ...and 11 more