6533b820fe1ef96bd1279160

RESEARCH PRODUCT

Sub-Finsler Horofunction Boundaries of the Heisenberg Group

Sebastiano Nicolussi GoloNate Fisher

subject

Pure mathematics20f69horoboundary53C23 (Primary) 20F18 20F65 (Secondary)Boundary (topology)Group Theory (math.GR)Heisenberg group01 natural sciencesdifferentiaaligeometriasub-finsler distanceMathematics - Metric Geometryhomogeneous group0103 physical sciencesFOS: MathematicsHeisenberg groupMathematics::Metric Geometry0101 mathematicsMathematicsQA299.6-433Applied Mathematics010102 general mathematicsryhmäteoriaheisenberg groupMetric Geometry (math.MG)53c2353c17Homogeneoussub-Finsler distance010307 mathematical physicsGeometry and TopologyMathematics - Group TheoryAnalysisWord (group theory)

description

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.

yearjournalcountryeditionlanguage
2020-09-14Analysis and Geometry in Metric Spaces
https://doi.org/10.1515/agms-2020-0121