EPFL  Ecole Polytechnique Fédérale de Lausanne

Publications by Marc Troyanov


Journal Articles Books and book chapters Conference papers and talks Thesis Teaching documents


Journal Articles



On three early papers by Herbert Busemann
Athanase Papadopoulos and  Marc Troyanov
To appear in  Herbert Busemann, Collected Works, ed. A. Papadopoulos, Springer Verlag 2017
https://arxiv.org/abs/1610.07372


On Pasch's Axiom and Desargues' Theorem in Busemann's work
Marc Troyanov
To appear  in  Herbert Busemann, Collected Works, ed. A. Papadopoulos, Springer Verlag 2017
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 ] 


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 Binet-Legendre Metric in Finsler Geometry.
V. Matveev and  M. Troyanov. 
Geometry & Topology 16 (2012) 2135–2170  [ 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 (2014), no. 4, 365–383 
[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.  [ / 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.  [ / 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 profile.
Bruce Hanson, Pekka Koskela, Marc Troyanov
Conform. Geom. Dyn. 2001 vol. 5 pp. 81-99 [ FullText / Link ]




An integral characterization of Hajłasz-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 ]




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 ]





Journal Articles Books and book chapters Conference papers and talks Thesis Teaching documents


Books and book chapters


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 ]



Conference papers and Talks


Piecewise flat Metrics on Surfaces and the Moduli Space.
M. Troyanov.
Oberwolfach Reports, vol. 3, num. 2, 2006, p. 1602     [ Full Text ]



Approximately Lipschitz Mappings and Sobolev Mappings between Metric Spaces.
Marc Troyanov,
in Proceedings on Analysis and Geometry, Sobolev Institute Press, Novosibirsk, (2000) 585–594.


Surfaces riemanniennes à singularités simples.
Marc Troyanov
in Differential geometry: geometry in mathematical physics and related topics (Los Angeles, CA, 1990), 619–628,
Proc. Sympos. Pure Math., 54, Part 2, Amer. Math. Soc., Providence, RI, 1993.  [ Link /

   
Metrics of constant curvature on a sphere with two conical singularities.
M. Troyanov.
Third International Symposium on Differential Geometry at Peñiscola 1988, Peñiscola, pages  296-306
Lecture Notes in Math., 1410, Springer, Berlin, 1989.  [Link / Fulltext]


Tangent Spaces to Metric Spaces: Overview and Motivations.
Marc Troyanov,
Séminaire Borel 2003 (IIIème Cycle Romand de Mathématiques), Berne. 2003  [ Full Text ]


Concentration et Inégalité de Poincaré.
Marc Troyanov,
Séminaire Borel 2001 (IIIème Cycle Romand de Mathématiques), Berne. 2001 [ Full Text ]


Thesis


Scaled Alexander-Spanier Cohomology and Lqp Cohomology for Metric Spaces
Genton, Luc
Thèse  EPFL, n° 6330, Lausanne 2014
Troyanov, Marc (dir.)  [Link]


Harmonic Maps on Smooth Metric Measure Spaces and on Riemannian Polyhedra
Sinaei, Zahra
Thèse  EPFL, n° 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.


Teaching Documents


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

   
Mesures et Intégration
M. Troyanov.
Ce document est un polycopié du cours de mesure et intégration que j'ai donné à l'EPFL durant les années 2003 à 2006. [ Full text ]


Dialogue Polynomial
M. Troyanov
Petit dialogue socratique pour étudiants, rédigé en 1992 en marge d'un cours d'algèbre (sur les anneaux et modules) donné à l'Université du Québec à Montréal. [ Full Text ]


Journal Articles Books and book chapters Conference papers and talks Thesis Teaching documents



Marc Troyanov
October 1, 2012