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math.GT2025
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…
math.GT2025
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…