Carnot-Carath\'{e}odory metrics associated to degenerate elliptic operators in three dimensions

Lyudmila Korobenko; Florian Meister; Olive Ross

Carnot-Carath\'{e}odory metrics associated to degenerate elliptic operators in three dimensions

Analysis of PDEs 2024-12-10 v1 Metric Geometry

Authors: Lyudmila Korobenko , Florian Meister , Olive Ross

Abstract

This note is a companion paper to arXiv:1608.01630 [math.CA]. Here we generalize some of the geometric results of arXiv:1608.01630 [math.CA] to the case of a $3\times 3$ matrix function $A(x)\approx \mathrm{diag}\{1,f(x_1), g(x_1)\}$ . More precisely, we make explicit calculations of the geodesics in the Carnot-Carath\'{e}odory space associated to $A$ , and provide estimates on the Lebesgue measures of metric balls centered at the origin in that space.

Keywords

Carnot-Carathéodory metric degenerate elliptic operator geodesics Lebesgue measure metric balls matrix function

Cite

@article{arxiv.2412.05810,
  title  = {Carnot-Carath\'{e}odory metrics associated to degenerate elliptic operators in three dimensions},
  author = {Lyudmila Korobenko and Florian Meister and Olive Ross},
  journal= {arXiv preprint arXiv:2412.05810},
  year   = {2024}
}

Carnot-Carath\'{e}odory metrics associated to degenerate elliptic operators in three dimensions

Abstract

Keywords

Cite

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