11 papers
Limit sets of mapping class groups
Hideki Miyachi, Ken'ichi Ohshika
We introduce the notions of horospherical limit point and big horospherical limit point in the projective measured foliation space for a subgroup of the mapping class group, which…
On the construction of geographical maps: Lagrange, Chebyshev, Darboux and Milnor
Hideki Miyachi, Ken'Ichi Ohshika, Athanase Papadopoulos
Lagrange, Chebyshev, and Darboux, in 1779, 1856, and 1911, respectively, wrote articles all bearing the same title, \emph{On the Construction of Geographical Maps}. In 1969, Milnor…
Convergence-Symmetric Metric Spaces
Ismail Saglam, Ken'Ichi Ohshika, Athanase Papadopoulos +1
We study some basic properties of spaces which satisfy the usual axioms of a metric space but without the symmetry axiom. We realised that such a study is needed in view of the rel…
The combinatorial structure of the unit tangent spheres and cotangent spheres of Teichm{ü}ller space with Thurston's Finsler metric
Ken'Ichi Ohshika, Athanase Papadopoulos
We prove several new results on the combinatorial structures of the unit spheres of the norms induced by Thurston's metric on the tangent and cotangent spaces of the Teichm{ü}ller…
On the Lambert conformal conical projection and the general map of the Russian Empire
Hideki Miyachi, Ken'Ichi Ohshika, Athanase Papadopoulos +1
The problem of drawing geographical maps is the one of mapping a subset of the sphere, representing a country or some other region on the surface of the Earth, into the Euclidean p…
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…
The horocyclic metric on Teichm{ü}ller spaces
Hideki Miyachi, Ken'Ichi Ohshika, Athanase Papadopoulos
In his paper Minimal stretch maps between hyperbolic surfaces, William Thurston defined a norm on the tangent space to Teichm{ü}ller space of a hyperbolic surface, which he called…
The earthquake metric on Teichm{ü}ller space
Yi Huang, Ken'ichi Ohshika, Huiping Pan +1
This is the first paper to systematically study the earthquake metric, an asymmetric Finsler metric on Teichm{ü}ller space introduced by Thurston. We provide proofs for several ass…