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.
Main Authors
Format
Articles
Research article
Published
2021
Series
Subjects
Publication in research information system
Publisher
De Gruyter
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202104072291Use this for linking
Review status
Peer reviewed
ISSN
2299-3274
DOI
https://doi.org/10.1515/agms-2020-0121
Language
English
Published in
Analysis and Geometry in Metric Spaces
Citation
- Fisher, N., & Nicolussi Golo, S. (2021). Sub-Finsler Horofunction Boundaries of the Heisenberg Group. Analysis and Geometry in Metric Spaces, 9(1), 19-52. https://doi.org/10.1515/agms-2020-0121
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Funder(s)
European Commission
Funding program(s)
FP7 (EU's 7th Framework Programme)
EU:n 7. puiteohjelma (FP7)
Funded by the European Union. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Education and Culture Executive Agency (EACEA). Neither the European Union nor EACEA can be held responsible for them.
Additional information about funding
S.N.G has been supported by the University of Padova STARS Project “Sub-Riemannian Geometry and Geometric Measure Theory Issues: Old and New”; by the INdAM – GNAMPA Project 2019 “Rectiability in Carnot
groups”; and by the Marie Curie Actions-Initial Training Network “Metric Analysis For Emergent Technologies
(MAnET)” (n. 607643).
Copyright© 2021 the Authors