Sub-Finsler Horofunction Boundaries of the Heisenberg Group
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
Published inAnalysis and Geometry in Metric Spaces
© 2021 the Authors
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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Related funder(s)European Commission
Funding program(s)FP7 (EU's 7th Framework Programme)
The content of the publication reflects only the author’s view. The funder is not responsible for any use that may be made of the information it contains.
Additional information about fundingS.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).
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