55 citations · 206 across the 33 of their papers we have counts for
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The Choreography of Geodesics in SOL
Marc Troyanov
We provide a self-contained geometric description of the geodesic flow in the three-dimensional Lie group , one of Thurston's eight model geometries. The geometry of…
Double Forms, Curvature Integrals and the Gauss-Bonnet Formula
Marc Troyanov
The Gauss-Bonnet Formula is a significant achievement in 19th century differential geometry for the case of surfaces and the 20th century cumulative work of H. Hopf, W. Fenchel, C.…
Riemannian Surfaces with Simple Singularities
Marc Troyanov
In this note we discuss the geometry of Riemannian surfaces having a discrete set of singular points. We assume the conformal structure extends through the singularities and the cu…
On Alexandrov's Surfaces with Bounded Integral Curvature
Marc Troyanov
During the years 1940-1970, Alexandrov and the "Leningrad School" have investigated the geometry of singular surfaces in depth. The theory developed by this school is about topolog…
Bernhard Riemann 1861 revisited: existence of flat coordinates for an arbitrary bilinear form
S. Bandyopadhyay, B. Dacorogna, V. S. Matveev +1
We generalize the celebrated results of Bernhard Riemann and Gaston Darboux: we give necessary and sufficient conditions for a bilinear form to be flat. More precisely, we give exp…
The Myers-Steenrod theorem for Finsler manifolds of low regularity
Vladimir S. Matveev, Marc Troyanov
We prove a version of Myers-Steenrod's theorem for Finsler manifolds under minimal regularity hypothesis. In particular we show that an isometry between -smooth (or partia…