Publications M. Troyanov

  • 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/1610.07372
  • On 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/1610.07959
  • The 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 ]
  • Cours de Géométrie.
    M. Troyanov.
    Presses Polytechniques et Universitaires Romandes (PPUR), 2009.
    ISBN: 978-2-88074-817-3
    [ Link / on googlebooks]
  • 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 ]
  • 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.