Plane Lorentzian and Fuchsian Hedgehogs

Canadian mathematical bulletin

Yves Martinez-Maure¹ 

[1] Institut Mathématique de Jussieu - Paris Rive Gauche, Bâtiment Sophie Germain, Case 7012, Paris Cedex 13, France

关键词: Fuchsian and Lorentzian hedgehogs;    evolute;    duality;    convolution;    reversed isoperimetric inequality;    reversed Bonnesen inequality;   

DOI  :  10.4153/CMB-2014-053-7

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

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

【 授权许可】

Unknown