Geodesic
Plane Lorentzian and Fuchsian Hedgehogs
Canadian mathematical bulletin, Tome 58 (2015) no. 3, pp. 561-574

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DOI

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).
DOI : 10.4153/CMB-2014-053-7
Mots-clés : 52A40, 52A55, 53A04, 53B30, Fuchsian and Lorentzian hedgehogs, evolute, duality, convolution, reversed isoperimetric inequality, reversed Bonnesen inequality 
Martinez-Maure, Yves. Plane Lorentzian and Fuchsian Hedgehogs. Canadian mathematical bulletin, Tome 58 (2015) no. 3, pp. 561-574. doi: 10.4153/CMB-2014-053-7
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     author = {Martinez-Maure, Yves},
     title = {Plane {Lorentzian} and {Fuchsian} {Hedgehogs}},
     journal = {Canadian mathematical bulletin},
     pages = {561--574},
     year = {2015},
     volume = {58},
     number = {3},
     doi = {10.4153/CMB-2014-053-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2014-053-7/}
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