Zobrazeno 1 - 10
of 126
pro vyhledávání: '"Troyanov, Marc"'
Autor:
Troyanov, Marc
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. B. Allendoerfer, A. Weil and S.S. Chern for higher-dimensional Rieman
Externí odkaz:
http://arxiv.org/abs/2308.15385
We revisit the isoperimetric inequalities for finitely generated groups introduced and studied by N. Varopoulos, T. Coulhon and L. Saloff-Coste. Namely we show that a lower bound on the isoperimetric quotient of finite subsets in a finitely generated
Externí odkaz:
http://arxiv.org/abs/2308.15376
Autor:
Troyanov, Marc
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 curvature is integrable. Such points are called \emph{simple singulariti
Externí odkaz:
http://arxiv.org/abs/2201.03359
Autor:
Troyanov, Marc
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 topological surfaces with an intrinsic metric for which we can define a notio
Externí odkaz:
http://arxiv.org/abs/2201.03354
We present a sharp version of the isoperimetric inequality for finitely generated groups due to T. Couhlon and L. Saloff-Coste based on the proof suggested by M. Gromov.
Comment: 7 pages
Comment: 7 pages
Externí odkaz:
http://arxiv.org/abs/2110.15798
Autor:
Troyanov, Marc
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 a forthcoming edition of Busemann's collected papers.
Externí odkaz:
http://arxiv.org/abs/1610.07959
Autor:
Papadopoulos, Athanase, Troyanov, Marc
This paper is a commentary and a reading guide to three papers by Herbert Busemann, \"Uber die Geometrien, in denen die "Kreise mit unendlichem Radius" die k\"urzesten Linien sind." (On the geometries where circles of infinite radius are the shortest
Externí odkaz:
http://arxiv.org/abs/1610.07372
Autor:
Matveev, Vladimir S., Troyanov, Marc
Publikováno v:
Proc. Amer. Math. Soc. 145 (2017), no. 6, 2699--2712
We prove a version of Myers-Steenrod's theorem for Finsler manifolds under minimal regularity hypothesis. In particular we show that an isometry between $C^{k,\alpha}$-smooth (or partially smooth) Finsler metrics, with $k+\alpha>0$, $k\in \mathbb{N}
Externí odkaz:
http://arxiv.org/abs/1605.03850
Autor:
Matveev, Vladimir S., Troyanov, Marc
We prove that any isometry between two dimensional Hilbert geometries is a projective transformation unless the domains are interiors of triangles.
Comment: 7 pages
Comment: 7 pages
Externí odkaz:
http://arxiv.org/abs/1409.5611
Autor:
Matveev, Vladimir S., Troyanov, Marc
Publikováno v:
European Journal of Mathematics 1 (2015), 483-502
The goal of this short paper is to give condition for the completeness of the Binet-Legendre metric in Finsler geometry. The case of the Funk and Hilbert metrics in a convex domain are discussed.
Comment: 17 pages, 3 figures
Comment: 17 pages, 3 figures
Externí odkaz:
http://arxiv.org/abs/1408.6401