29 citations · 33 across the 6 of their papers we have counts for
6 papers
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…
On the -cohomology of Riemannian Manifolds with Negative Curvature
Vladimir Gol'dshtein, Marc Troyanov
We prove a non-vanishing result for the -cohomology of complete simply-connected Riemannian manifolds with pinched negative curvature.
Distortion of Mappings and -Cohomology
Vladimir Gol'dshtein, Marc Troyanov
We study some relation between some geometrically defined classes of diffeomorphisms between manifolds and the -cohomology of these manifolds. Some applications to vanishi…
On the naturality of the exterior differential
Vladimir Gol'dshtein, Marc Troyanov
We give sufficient conditions for the naturallity of the exterior differential under Sobolev mappings. In other words we study the validity of the equation for a…
A Conformal de Rham Complex
Vladimir Gol'dshtein, Marc Troyanov
We introduce the notion of a conformal de Rham complex of a Riemannian manifold. This is a graded differential Banach algebra and it is invariant under quasiconformal maps, in part…
On the Moduli Space of Singular Euclidean Surfaces
Marc Troyanov
The goal of this paper is to develop some aspects of the deformation theory of piecewise flat structures on surfaces and use this theory to construct new geometric structures on th…