Analysis and Geometry in Metric Spaces (Mar 2021)

Sub-Finsler Horofunction Boundaries of the Heisenberg Group

  • Fisher Nate,
  • Golo Sebastiano Nicolussi

DOI
https://doi.org/10.1515/agms-2020-0121
Journal volume & issue
Vol. 9, no. 1
pp. 19 – 52

Abstract

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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.

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