Carnot-Carath\'eodory metrics associated to degenerate elliptic operators in three dimensions
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× 3 matrix function A(x)≈ diag\1,f(x1), g(x1)\. More precisely, we make explicit calculations of the geodesics in the Carnot-Carath\'eodory space associated to A, and provide estimates on the Lebesgue measures of metric balls centered at the origin in that space.
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