55 citations · 206 across the 33 of their papers we have counts for
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On Pasch's Axiom and Desargues' Theorem in Busemann's work
Marc Troyanov
In this note, we discuss the role played by the techniques from the "foundations of geometry" and in particular by Desargues' Theorem in the work of Busemann. This note is part of…
On three early papers by Herbert Busemann
Athanase Papadopoulos, Marc Troyanov
This paper is a commentary and a reading guide to three papers by Herbert Busemann, Über die Geometrien, in denen die "Kreise mit unendlichem Radius" die kürzesten Linien sind." (O…
Isometries of two dimensional Hilbert Geometries
Vladimir S. Matveev, Marc Troyanov
We prove that any isometry between two dimensional Hilbert geometries is a projective transformation unless the domains are interiors of triangles.
From Funk to Hilbert Geometry
Athanase Papadopoulos, Marc Troyanov
We survey some basic geometric properties of the Funk metric of a convex set in . In particular, we study its geodesics, its topology, its metric balls, its convexity…
Harmonic symmetrization of convex sets and of Finsler structures, with applications to Hilbert geometry
Athanase Papadopoulos, Marc Troyanov
David Hilbert discovered in 1895 an important metric that is canonically associated to any convex domain in the Euclidean (or projective) space. This metric is known to be Fins…
Weak metrics on Euclidean domains
Athanase Papadopoulos, Marc Troyanov
A weak metric on a set is a function that satisfies the axioms of a metric except the symmetry and the separation axioms. In the present paper we introduced a weak metric, called t…