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Bisecting measures with hyperplane arrangements

Part of: Discrete geometry Classical Topics in Algebraic Topology

Published online by Cambridge University Press:  31 October 2019

ALFREDO HUBARD  and
ROMAN KARASEV
ALFREDO HUBARD
Affiliation:
Université Paris-Est Marne-la-Vallée, LIGM. UMR 8049, CNRS, ENPC, ESIEE, UPEM, F- 77454, Marne-la-Vallée, France. e-mail : alfredo.hubard@u-pem.fr
ROMAN KARASEV
Affiliation:
Moscow Institute of Physics and Technology, Institutskiy per. 9, Dolgoprudny, Russia 141700. Institute for Information Transmission Problems RAS, Bolshoy Karetny per. 19, Moscow, Russia 127994. e-mail : r_n_karasev@mail.ru
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Abstract

We show that provided that n is a power of two, any nD measures in ℝn can be bisected by an arrangement of D hyperplanes.

MSC classification

Primary: 52C35: Arrangements of points, flats, hyperplanes 55M20: Fixed points and coincidences 55M35: Finite groups of transformations (including Smith theory)
Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 169 , Issue 3 , November 2020 , pp. 639 - 647
Copyright
© Cambridge Philosophical Society 2020

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References

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