Sub-Finsler Horofunction Boundaries of the Heisenberg Group

Sub-Finsler Horofunction Boundaries of the Heisenberg Group

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 b...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Analysis and Geometry in Metric Spaces 2021-01, Vol.9 (1), p.19-52
Hauptverfasser: Fisher, Nate, Golo, Sebastiano Nicolussi
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
Physical Sciences
Science & Technology
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung: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.
ISSN:2299-3274
2299-3274
DOI:10.1515/agms-2020-0121