arXiv Open Access 2024

Carnot-Carathéodory metrics associated to degenerate elliptic operators in three dimensions

Lyudmila Korobenko Florian Meister Olive Ross

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Abstrak

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-Carathéodory space associated to $A$, and provide estimates on the Lebesgue measures of metric balls centered at the origin in that space.

Topik & Kata Kunci

math.AP math.MG

Penulis (3)

Lyudmila Korobenko

Florian Meister

Olive Ross

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APA MLA BibTeX

Korobenko, L., Meister, F., Ross, O. (2024). Carnot-Carathéodory metrics associated to degenerate elliptic operators in three dimensions. https://arxiv.org/abs/2412.05810

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Informasi Jurnal

Tahun Terbit: 2024
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓