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arXiv · 2009.06820

Sub-Finsler horofunction boundaries of the Heisenberg group

Nate Fisher·Sebastiano Nicolussi Golo
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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.

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Nate Fisher, Sebastiano Nicolussi Golo. 2020-09-15. Sub-Finsler horofunction boundaries of the Heisenberg group. https://arxiv.org/abs/2009.06820

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