Marc Troyanov
Il - He/him
EPFL SB-DO
MA A1 365 (Bâtiment MA)
Station 8
1015 Lausanne
Office:
MA A1 365
EPFL › VPA › VPA-AVP-DLE › AVP-DLE-EDOC › EDMA-ENS
Expertise
Theses
Scaled Alexander-Spanier Cohomology and Lqp Cohomology for Metric Spaces
Genton, Luc
Thèse EPFL, 6330, Lausanne 2014
Troyanov, Marc (dir.) [Link]
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 ]
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]
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]
Ducret Stephen ; Troyanov, Marc (dir.) Lausanne : EPFL, 2009. [Link / fulltext]
Regularity in metric spaces
Timochine, Serguei ; Troyanov, Marc (dir.) Lausanne : EPFL, 2006. [Link / fulltext]
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]
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]
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.
Troyanov, Marc ; Haefliger, André (Dir.) Université de Genève, 1987.
Livres et chapitres de livres
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]
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 ]
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/1610.07372
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
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 ]
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 ]
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 ]
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]
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]
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]
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]
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]
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]
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 ]
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 ]
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 ]
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 ]
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 ]
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 ]
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
]
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 ]
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
]
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 ]
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 ]
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 ]
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 ]
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 ]
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 ]
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 ]
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 ]
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 ]
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 ]
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 ]
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 ]
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 ]
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 ]
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 ]
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 ]
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 ]
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 ]
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 ]
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 ]
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 ]
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 ]
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 ]
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 ]
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 ]
D. Hulin et M. Troyanov,
C.R. Acad. Sci. Paris, 310 (1990) 203-206. [ 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.
Domaine de recherche : géométrie différentielle, analyse sur les variétés et sur les espaces métriques.
Enseignement et PhD
A dirigé les thèses EPFL de
Olivier Mermoud (2000), Khaled Gafaiti (2001), Serguei Timochine (2006), Stephen Ducret (2009), Ratiba Djelid (2011), Zahra Sinaei (2013), Luc Genton (2014), Adrien Giuliano Marcone (2019), Guillaume Buro (2023), Bruno Luiz Santos Correia (2025)