Search results for "sub-finsler distance"

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Sub-Finsler Horofunction Boundaries of the Heisenberg Group

2020

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.

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)Analysis and Geometry in Metric Spaces
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