Analysis and Geometry in Metric Spaces (Mar 2021)
Sub-Finsler Horofunction Boundaries of the Heisenberg Group
Abstract
We give a complete analytic and geometric description of the horofunction boundary for polygonal sub-Finsler metrics, that is, those that arise as asymptotic cones of word metrics, on the Heisenberg group. We develop theory for the more general case of horofunction boundaries in homogeneous groups by connecting horofunctions to Pansu derivatives of the distance function.
Keywords