Marc Troyanov

Expertise Géométrie DifférentielleAnalyse géométriqueORCID # 0000-0002-4912-0711 [Link] Theses Scaled Alexander-Spanier Cohomology and Lqp Cohomology for Metric Spaces Genton, Luc Thèse  EPFL, 6330, Lausanne 2014 Troyanov, Marc (dir.)  [Link]Harmonic Maps on Smooth Metric Measure Spaces and on Riemannian Polyhedra Sinaei, Zahra Thèse  EPFL, 5790, Lausanne 2013 Troyanov, Marc (dir.)  [Link ]Déformations conformes des variétés de Finsler-Ehresmann Ratiba Djelid Thèse EPFL, no 5032 (2011). Dir.: Marc Troyanov. [Link / fulltext]Lq,p-cohomology of Riemannian manifolds and simplicial complexes of bounded geometry Ducret Stephen ; Troyanov, Marc (dir.) Lausanne : EPFL, 2009.  [Link / fulltext]Regularity in metric spaces Timochine, Serguei ; Troyanov, Marc (dir.) Lausanne : EPFL, 2006.  [Link / fulltext]Algèbres de Royden et homéomorphismes à p-dilatation bornée entre espaces métriques mesurés Gafaiti, Khaled ; Troyanov, Marc (dir.) Lausanne : EPFL, 2001. [Link / fulltext]Méthodes de géométrie différentielle en théorie des mécanismes Mermoud, Olivier ; Troyanov, Marc (dir.) Lausanne : EPFL, 2000. [Link / fulltext]Les surfaces riemanniennes à singularités coniques Troyanov, Marc ; Haefliger, André (Dir.) Université de Genève, 1987. Livres et chapitres de livres Cours de Géométrie. M. Troyanov.EPFL Press, 2009-2025.  [ Link]On the moduli space of singular Euclidean surfaces. M. Troyanov in: Handbook of Teichmüller Theory, Volume 1, 2007, p. 507-540 Eur. Math. Soc., Zürich, 2007. ISBN: 978-3-03719-029-6 [Abstract / Full text]Espaces à courbure négative et groupes hyperboliques. M. Troyanov. in Sur les groupes hyperboliques d’après Mikhael Gromov, 1990, p. 47-66 Boston : Birkhäuser , 1990. ISBN: 0-8176-3508-4 [ Link / An unofficial English translation ] Publication On three early papers by Herbert Busemann Athanase Papadopoulos and  Marc Troyanov in Herbert Busemann, Collected Works, ed. A. Papadopoulos, Springer Verlag 2018 https://arxiv.org/abs/1610.07372On Pasch’s Axiom and Desargues’ Theorem in Busemann’s work Marc Troyanov in  Herbert Busemann, Collected Works, ed. A. Papadopoulos, Springer Verlag 2018 https://arxiv.org/abs/1610.07959The Myers-Steenrod theorem for Finsler manifolds of low regularity Proc. Amer. Math. Soc. 145 (2017), pp. 2699-2712. [ FullText / Link ] Isometries of two dimensional Hilbert geometries V. Matveev and  M. Troyanov.Enseign. Math. 61 (2015), no. 3-4, 453–460.   [ FullText / Link ] Completeness and incompleteness of the Binet-Legendre metric V. Matveev and  M. Troyanov.Eur. J. Math. 1 (2015), no. 3, 483–502.   [ FullText / Link ] The connectivity at infinity of a manifold supporting an Lq,p-Sobolev inequality Stefano Pigola, Alberto G Setti and Marc Troyanov Expo. Math. 32 (2015), no. 4, 365–383  [FullText / Link]Weak Minkowski Spaces Athanase Papadopoulos and Marc Troyanov Handbook of Hilbert geometry, Chapter 1, IRMA Lect. Math. Theor. Phys.,  Zürich, 2014, pp. 11–32  [FullText / Link]From Funk to Hilbert geometry Athanase Papadopoulos and Marc Troyanov Handbook of Hilbert geometry, Chapter 2, IRMA Lect. Math. Theor. Phys.,  Zürich, 2014, pp. 33-67   [FullText / Link]Funk and Hilbert geometries from the Finslerian Viewpoint Marc Troyanov Handbook of Hilbert geometry, Chapter 3, IRMA Lect. Math. Theor. Phys.,  Zürich, 2014, pp 69-110  [FullText / Link]On the origin of Hilbert geometry Marc Troyanov Handbook of Hilbert geometry, Chapter 14, IRMA Lect. Math. Theor. Phys.,  Zürich, 2014, pp 383–389  [FullText / Link]The connectivity at infinity of a manifold supporting an Lq,p-Sobolev inequality Stefano Pigola, Alberto G Setti and Marc Troyanov Expo. Math. 32 (2015), no. 4, 365–383  [FullText / Link]The Binet-Legendre Metric in Finsler Geometry. V. Matveev and  M. Troyanov.Geometry & Topology 16 (2012) 2135–2170  [ FullText / Link ]   The Hölder-Poincaré duality for Lq,p-cohomology. V. Goldshtein and M. Troyanov. Annals of Global Analysis and Geometry (2012), Volume 41, Issue 1, pp 25-45 [ FullText / Link ]A short proof of the Hölder-Poincaré duality for Lp-cohomology. V. Goldshtein and M. Troyanov. Rend. Semin. Mat. Univ. Padova 124 (2010), 179–184. [ FullText / Link ]A Conformal de Rham Complex. V. Goldshtein and M. Troyanov. Journal of Geom. Anal.,  (2010), 20,  651–669 [ FullText / Link ] On the Hodge decomposition in R^n. M. Troyanov. Moscow Mathematical Journal Vol. 9, No 4, (2009), 899–926. [ FullText / Link ]Les surfaces à courbure intégrale bornée au sens d’Alexandrov. M. Troyanov. arXiv:0906.3407v1 [math.DG], 2009. [ FullText / Link ]Distortion of Mappings and Lq,p-Cohomology. V. Goldshtein and M. Troyanov. Mathematische Zeitschrift 264 (2010), 279-293. [ FullText / Link ]Weak Finsler structures and the Funk weak metric. A. Papadopoulos and M. Troyanov. Mathematical Proceedings of the Cambridge Philosophical Society, (2009), 147: 419-437 [ FullText / Link ]Harmonic symmetrization of convex sets and of Finsler structures, with applications to Hilbert geometry. A. Papadopoulos and M. Troyanov. Expositiones Mathematica, 27(2): 109-124, 2009. [ FullText / Link ]Finsler Conformal Lichnerowicz-Obata conjecture.   V. Matveev, H.-B. Rademacher, M. Troyanov, and A. Zeghib. Annales de l’institut Fourier, 59(3): 937-949, 2009. [ FullText / Link ]Lq,p-cohomology of Riemannian Manifolds with Negative Curvature.  M. Troyanov and V. Goldshtein. In V. Maz’ya, editor, Sobolev Spaces in Mathematics, volume II.International Mathematical Series, pages 199-208. Springer, New York, 2009. [ Full Text / Link ]On the naturality of the exterior differential.  V. Goldshtein and M. Troyanov. C. R. Math. Rep. Acad. Sci. Canada, 30(1):1-10, 2008. [ Full Text ]Steiner’s Invariants and Minimal Connections. Ducret Stephen,Troyanov Marc Portugaliae Mathematica, vol. 65, num. 2, (2008), p. 237–242. [ Full Text / Link ]Weak metrics on Euclidean domains Papadopoulos, Athanase ; Troyanov, Marc JP Journal of Geometry and Topology, vol. 7, num. 1, 2007, p. 23 – 44. [ FullText / Link ] Sobolev inequalities for differential forms and  L_qp cohomology. Gol’dshtein, Vladimir ; Troyanov, Marc J. Geom. Anal., vol. 16, num. 4, 2006, p. 597-631.  [ FullText / Link ]Thurston’s weak metric on the Teichmüller space of the Torus. Belkhirat, Abdelhadi ; Papadopoulos, Athanase ; Troyanov, Marc Trans. Am. Math. Soc., vol. 357, num. 8, 2005, p. 3311-3324.   [ FullText / Link ]Mean curvature and asymptotic volume of small balls. Hulin, Dominique ; Troyanov, Marc American Mathematical Monthly  vol. 110, num. 10, 2003, p. 947-950.  [ FullText / Link ]Liouville type theorems for mappings with bounded (co)-distortion. Troyanov, Marc ; Vodop’yanov, Sergei Ann. Inst. Fourier, vol. 52, num. 6, 2002, p. 1753-1784.  [ FullText / Link ]Capacities in metric spaces. Gol’dshtein, Vladimir ; Troyanov, Marc Integral Equations Oper. Theory, vol. 44, num. 2, 2002, p. 212-242.  [ FullText / Link ]Voronoi diagrams on piecewise flat surfaces and an application to biological growth.  Indermitte, C ; Troyanov, M ; Clémencon, H ; Liebling, H Theoretical Computer Scienc, vol. 263, num. 1-2, 2001, p. 268 – 274.  [ FullText / Link ]Axiomatic theory of Sobolev spaces. Gol’dshtein, Vladimir ; Troyanov, Marc Expo. Math., vol. 19, num. 4, 2001, p. 289-336.  [ FullText / Link ]Boundary behavior of quasi-regular maps and the isodiametric Books-and-book-chapters. Bruce Hanson, Pekka Koskela, Marc Troyanov Conform. Geom. Dyn. 2001 vol. 5 pp. 81-99 [ FullText / Link ]An integral characterization of Hajlasz-Sobolev space. Gol’dshtein, Vladimir ; Troyanov, Marc C. R. Acad. Sci. Paris Sér. I Math. (2001) vol. 333 (5) pp. 445-450  [ FullText / Link ]Solving the p-Laplacian on Manifolds. Marc Troyanov, Proc. Amer. Math. Soc. 128 (2000) 541–545.  [ FullText / Link ]Approximately Lipschitz Mappings and Sobolev Mappings between Metric Spaces. Marc Troyanov, in Proceedings on Analysis and Geometry, Sobolev Institute Press, Novosibirsk, (2000) 585–594. [ FullText ]Parabolicity of Manifolds. Marc Troyanov Siberian Advances in Mathematics 9 (1999) 125–150.  [ FullText / Link ]The Kelvin-Nevanlinna-Royden criterion for p-parabolicity. Vladimir Gol’dshtein and Marc Troyanov Mathematische Zeitschrift 232 (1999). 607–619. [ FullText / Link ]Sur la non résolubilité du p-laplacien sur R^n. V. Gol’dshtein and M. Troyanov, C.R. Acad. Sci. Paris, 326 (1998) 1185–1186  [ FullText / Link ]The Lpq-Cohomology of SOL. V. Gol’dshtein and M. Troyanov Annales de la Faculté des Sciences de Toulouse, tom. VII (1998) 687-698. [ FullText / Link ]L’Horizon de SOL. Marc Troyanov Expositiones Mathematicae, 16 (1998) p. 441-479.  [ FullText / Link ]Prescribing curvature on open surfaces. Dominique Hulin et Marc Troyanov Math. Ann. 293 (1992), no. 2, 277–315.  [ FullText / Link ]The Schwarz lemma for non positively curved Riemannian surfaces. M. Troyanov, Manuscripta Mathematica 72 (1991) 251-256.  [ FullText / Link ]Prescribing Curvature on Compact Surfaces with Conical singularities. M. Troyanov, Trans. Amer. Math. Soc. 324 (1991) 793-821.  [ FullText / Link ]Un principe de concentration-compacité pour les suites de surfaces riemanniennes. M. Troyanov, Ann. Inst. Henri Poincaré – Analyse non linéaire, 8 (1991) 419–441.  [ FullText / Link ]Sur la courbure des surfaces ouvertes. D. Hulin et M. Troyanov, C.R. Acad. Sci. Paris, 310 (1990) 203-206.  [ FullText / Link ]Coordonnées polaires sur les surfaces riemanniennes singulières. M. Troyanov, Ann. Inst. Fourier, 40 (1990) 913-937.  [ FullText / Link ]Les surfaces euclidiennes à singularités coniques.  M. Troyanov Enseign. Math. (2) (1986) vol. 32 (1-2) pp. 79-94  [ FullText / Link ] Doctorat en mathématiques à l'Université de Genève (1987) - Postdoc à Paris et Salt-Lake City, puis professeur assistant à l'UQAM (Montréal). Venu en 1993 à l'EPFL comme professeur assistant, nommé MER en 1999 puis professeur titulaire en 2005. Professeur Honoraire depuis 2025.Domaine de recherche : géométrie différentielle, analyse sur les variétés et sur les espaces métriques. RecherchePublications Lien vers mes publications Enseignement et PhD A dirigé les thèses EPFL de Olivier Mermoud, Khaled Gafaiti, Serguei Timochine, Stephen Ducret, Ratiba Djelid, Zahra Sinaei, Luc Genton, Adrien Giuliano Marcone, Guillaume Buro, Bruno Luiz Santos Correia Cours Algèbre linéaire avancée II MATH-115(b) L'objectif du cours est d'introduire les notions de base de l'algèbre linéaire et de démontrer rigoureusement les résultats principaux du sujet.