8 papers
Some inequalities for tetrahedra
Jin-ichi Itoh, Joël Rouyer, Costin Vîlcu
We prove inequalities involving intrinsic and extrinsic radii and diameters of tetrahedra.
Farthest points on flat surfaces
Joël Rouyer, Costin Vîlcu
We consider the distance function from an arbitrary point on a flat surface, and determine the set of all \emph{farthest points} (i.e., points at maximal distance) from…
Double normals of most convex bodies
Alain Rivière, Joël Rouyer, Costin Vîlcu +1
We consider a typical (in the sense of Baire categories) convex body in . The set of feet of its double normals is a Cantor set, having lower box-counting dim…
Steinhaus conditions for convex polyhedra
Joël Rouyer
On a convex surface , the antipodal map associates to a point the set of farthest points from , with respect to the intrinsic metric. is called a Steinhaus surfac…
Farthest points on most Alexandrov surfaces
Joël Rouyer, Costin Vîlcu
We study global maxima of distance functions on most Alexandrov surfaces with curvature bounded below, where "most" is used in the sense of Baire categories.
Simple closed geodesics on most Alexandrov surfaces
Joël Rouyer, Costin Vîlcu
We study the existence of simple closed geodesics on most (in the sense of Baire category) Alexandrov surfaces with curvature bounded below, compact and without boundary. We show t…
The connected components of the space of Alexandrov surfaces
Joël Rouyer, Costin Vîlcu
Denote by the set of all compact Alexandrov surfaces with curvature bounded below by without boundary, endowed with the topology induced by the Gromov-Hausdorf…
Sets of tetrahedra, defined by maxima of distance functions
Joël Rouyer, Costin Vîlcu
We study tetrahedra and the space of tetrahedra from the viewpoint of local and global maxima for intrinsic distance functions.