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Plane Lorentzian and Fuchsian Hedgehogs

Published online by Cambridge University Press:  20 November 2018

Yves Martinez-Maure*
Affiliation:
Institut Mathématique de Jussieu - Paris Rive Gauche, Bâtiment Sophie Germain, Case 7012, Paris Cedex 13, France e-mail: yves.martinez-maure@imj-prg.fr
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Abstract

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Parts of the Brunn–Minkowski theory can be extended to hedgehogs, which are envelopes of families of affine hyperplanes parametrized by their Gauss map. F. Fillastre introduced Fuchsian convex bodies, which are the closed convex sets of Lorentz–Minkowski space that are globally invariant under the action of a Fuchsian group. In this paper, we undertake a study of plane Lorentzian and Fuchsian hedgehogs. In particular, we prove the Fuchsian analogues of classical geometrical inequalities (analogues that are reversed as compared to classical ones).

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2015

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