5 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…
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…
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 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…