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BY 4.0 license Open Access Published by De Gruyter Open Access March 30, 2021

Sub-Finsler Horofunction Boundaries of the Heisenberg Group

  • Nate Fisher and Sebastiano Nicolussi Golo EMAIL logo

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.

MSC 2010: 20F69; 53C23; 53C17

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Received: 2020-10-24
Accepted: 2021-01-13
Published Online: 2021-03-30

© 2021 Nate Fisher et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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