1. CMB 2014 (vol 58 pp. 561)
 MartinezMaure, Yves

Plane Lorentzian and Fuchsian Hedgehogs
Parts of the BrunnMinkowski 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 LorentzMinkowski 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 which
are reversed as compared to classical ones).
Keywords:Fuchsian and Lorentzian hedgehogs, evolute, duality, convolution, reversed isoperimetric inequality, reversed Bonnesen inequality Categories:52A40, 52A55, 53A04, 53B30 

2. CMB 1997 (vol 40 pp. 108)
 Schaer, J.

Continuous Selfmaps of the Circle
Given a continuous map $\delta$ from the circle $S$ to itself we
want to find all selfmaps $\sigma\colon S\to S$ for which
$\delta\circ\sigma = \delta$. If the degree $r$ of $\delta$ is not
zero, the transformations $\sigma$ form a subgroup of the cyclic
group $C_r$. If $r=0$, all such invertible transformations form a
group isomorphic either to a cyclic group $C_n$ or to a dihedral
group $D_n$ depending on whether all such transformations are
orientation preserving or not. Applied to the tangent image of
planar closed curves, this generalizes a result of Bisztriczky and
Rival [1]. The proof rests on the theorem: {\it Let
$\Delta\colon\bbd R\to\bbd R$ be continuous, nowhere constant, and
$\lim_{x\to \infty}\Delta(x)=\infty$, $ \lim_{x\to+\infty}\Delta
(x)=+\infty$; then the only continuous map $\Sigma\colon\bbd R\to\bbd
R$ such that $\Delta\circ\Sigma=\Delta$ is the identity
$\Sigma=\id_{\bbd R}$.
Categories:53A04, 55M25, 55M35 
