4 papers · 1 filter
On families of Finsler metrics
Ismail Saglam, Ken'Ichi Ohshika, Athanase Papadopoulos
In this paper, we answer some natural questions on symmetrisation and more general combinations of Finsler metrics, with a view towards applications to Funk and Hilbert geometries…
On spaces of Euclidean triangles and triangulated Euclidean surfaces
Ismail Saglam, Ken'Ichi Ohshika, Athanase Papadopoulos
In this paper, we introduce an asymmetric distance function on the space of marked Euclidean triangles of normalised area, and we prove several properties of this metric, which tur…
On the Marinus--Ptolemy and Delisle--Euler conical maps
Hideki Miyachi, Ken'Ichi Ohshika, Athanase Papadopoulos
We examine connections between the mathematics behind methods of drawing geographical maps due, on the one hand to Marinos and Ptolemy (1st-2nd c. CE) and on the other hand to Deli…
Convex structures of the unit tangent spheres in Teichm{ü}ller space
Assaf Bar-Natan, Ken'Ichi Ohshika, Athanase Papadopoulos
We analyse the convex structure of the Finsler infinitesimal balls of the Thurston metric on Teichm{ü}ller space. We analyse the convex structure of the Finsler unit ball in the ta…