Research group publications


Semiclassical Estimates for Eigenvalue Means of Laplacians on Spheres

D. Buoso; P. Luzzini; L. Provenzano; J. Stubbe 

Journal Of Geometric Analysis. 2023-09-01. Vol. 33, num. 9, p. 280. DOI : 10.1007/s12220-023-01326-6.

The first Grushin eigenvalue on cartesian product domains

P. Luzzini; L. Provenzano; J. Stubbe 

Advances In Calculus Of Variations. 2023-03-31. DOI : 10.1515/acv-2022-0015.

Les géodésiques des métriques finslériennes et pseudo-finslériennes faibles de basse régularité

G. Buro / M. Troyanov (Dir.)  

Lausanne, EPFL, 2023. 


On the equation (Du)(t) H Du = G

S. Bandyopadhyay; B. Dacorogna; V. Matveev; M. Troyanov 

Nonlinear Analysis-Theory Methods & Applications. 2022-01-01. Vol. 214, p. 112554. DOI : 10.1016/


Complementary Asymptotically Sharp Estimates for Eigenvalue Means of Laplacians

E. M. Harrell; L. Provenzano; J. Stubbe 

International Mathematics Research Notices. 2021-06-01. Vol. 2021, num. 11, p. 8405-8450. DOI : 10.1093/imrn/rnz085.

On the spectral asymptotics for the buckling problem

D. Buoso; P. Luzzini; L. Provenzano; J. Stubbe 

Journal Of Mathematical Physics. 2021-12-01. Vol. 62, num. 12, p. 121501. DOI : 10.1063/5.0069529.


Regularity of solutions for a fourth-order elliptic system via Conservation law

C-Y. Guo; C-L. Xiang 

Journal of the London Mathematical Society-Second Series. 2020. Vol. 101, num. 3, p. 907-922. DOI : 10.1112/jlms.12289.


Warped tori with almost non-negative scalar curvature

B. Allen; L. Hernandez-Vazquez; D. Parise; A. Payne; S. Wang 

Geometriae Dedicata. 2019-06-01. Vol. 200, num. 1, p. 153-171. DOI : 10.1007/s10711-018-0365-y.

A Gauss-Bonnet Theorem for Asymptotically Conical Manifolds and Manifolds with Conical Singularities

A. G. Marcone / M. Troyanov (Dir.)  

Lausanne, EPFL, 2019. 


Detecting Anisotropic Inclusions Through EIT

J. Cristina; L. Paivarinta 

Archive For Rational Mechanics And Analysis. 2017. Vol. 226, num. 3, p. 1139-1160. DOI : 10.1007/s00205-017-1151-y.

The Myers-Steenrod Theorem For Finsler Manifolds Of Low Regularity

V. S. Matveev; M. Troyanov 

Proceedings Of The American Mathematical Society. 2017. Vol. 145, num. 6, p. 2699-2712. DOI : 10.1090/proc/13407.


Minkowski space is locally the Noldus limit of Poisson process causets

J. Cristina 

Classical And Quantum Gravity. 2016. Vol. 33, num. 17, p. 175008. DOI : 10.1088/0264-9381/33/17/175008.

Minimal entropy for uniform lattices in product of hyperbolic planes

L. Merlin 

Commentarii Mathematici Helvetici. 2016. Vol. 91, num. 1, p. 107-129. DOI : 10.4171/Cmh/379.


The connectivity at infinity of a manifold and Sobolev inequalities

S. Pigola; A. G. Setti; M. Troyanov 

Expositiones Mathematicae. 2014. Vol. 32, num. 4, p. 365-383. DOI : 10.1016/j.exmath.2013.12.006.

Scaled Alexander-Spanier Cohomology and Lqp Cohomology for Metric Spaces

L. Genton / M. Troyanov (Dir.)  

Lausanne, EPFL, 2014. 

Sharp estimates on the first eigenvalue of the p-Laplacian with negative Ricci lower bound

A. Naber; D. Valtorta 

Mathematische Zeitschrift. 2014. Vol. 277, num. 3-4, p. 867-891. DOI : 10.1007/s00209-014-1282-x.


Harmonic Maps on Smooth Metric Measure Spaces and on Riemannian Polyhedra

Z. Sinaei / M. Troyanov (Dir.)  

Lausanne, EPFL, 2013. 


The Holder-Poincaré duality for Lqp-cohomology

V. Gol’dshtein; M. Troyanov 

Annals Of Global Analysis And Geometry. 2012. Vol. 41, p. 25-45. DOI : 10.1007/s10455-011-9269-x.


The corona theorem for the Drury–Arveson Hardy space and other holomorphic Besov–Sobolev spaces on the unit ball in C-n

S. Costea; E. T. Sawyer; B. D. Wick 

Analysis & Pde. 2011. Vol. 4, p. 499-550. DOI : 10.2140/apde.2011.4.499.

Déformations conformes des variétés de Finsler-Ehresmann

R. Djelid / M. Troyanov (Dir.)  

Lausanne, EPFL, 2011. 


A Short Proof of the Holder-Poincare Duality for Lp-Cohomology

V. Gol’dshtein; M. Troyanov 

Rendiconti Del Seminario Matematico Della Universita Di Padova. 2010. Vol. 124, p. 179-184.

A Conformal de Rham Complex

V. Gol’Dshtein; M. Troyanov 

Journal of Geometric Analysis. 2010. Vol. 20, num. 3, p. 651-669. DOI : 10.1007/s12220-010-9119-2.


On the Hodge decomposition in $\mathbb{R}^n$

M. Troyanov 

Moscow Mathematical Journal. 2009. Vol. 9, num. 4, p. 899-926.

Lq,p-cohomology of Riemannian manifolds and simplicial complexes of bounded geometry

S. Ducret / M. Troyanov (Dir.)  

Lausanne, EPFL, 2009. 

Les surfaces à courbure intégrale bornée au sens d’Alexandrov

M. Troyanov 

ArXiv. 2009. Vol. arXiv:0906.3407v1 [math.DG].

Distortion of Mappings and $L_{q,p}$-Cohomology

V. Goldshtein; M. Troyanov 

Mathematische Zeitschrift. 2009. Vol. 264, p. 279. DOI : 10.1007/s00209-008-0463-x.

Weak Finsler structures and the Funk weak metric

A. Papadopoulos; M. Troyanov 

Mathematical Proceedings of the Cambridge Philosophical Society. 2009. Vol. 147, num. 2, p. 419–437. DOI : 10.1017/S0305004109002461.

Harmonic symmetrization of convex sets and of Finsler structures, with applications to Hilbert geometry

A. Papadopoulos; M. Troyanov 

Expositiones Mathematica. 2009. Vol. 27, num. 2, p. 109-124. DOI : 10.1016/j.exmath.2008.10.001.

Finsler Conformal Lichnerowicz-Obata conjecture

V. Matveev; H-B. Rademacher; M. Troyanov; A. Zeghib 

Annales de l’institut Fourier. 2009. Vol. 59, num. 3, p. 937-949. DOI : 10.5802/aif.2452.

$L_{q,p}$-cohomology of Riemannian Manifolds with Negative Curvature

M. Troyanov; V. Goldshtein 

Sobolev Spaces in Mathematics; New York: Springer, 2009. p. 199-208.

Cour de géométrie

M. Troyanov 

Lausanne: Presses Polytechniques et Universitaires Romandes (PPUR), 2009.


On the naturality of the exterior differential

V. Goldshtein; M. Troyanov 

C. R. Math. Rep. Acad. Sci. Canada. 2008. Vol. 30, num. 1, p. 1-10.

Mesures et Intégration

M. Troyanov 


Steiner’s Invariants and Minimal Connections

S. Ducret; M. Troyanov 

Portugaliae Mathematica. 2008. Vol. 65, num. 2, p. 237-242.


On the moduli space of singular Euclidean surfaces

M. Troyanov 

Handbook of Teichmüller theory.; Zürich: Eur. Math. Soc., Zürich, 2007. p. 507-540.

Weak metrics on Euclidean domains

A. Papadopoulos; M. Troyanov 

JP Journal of Geometry and Topology. 2007. Vol. 7, num. 1, p. 23-44.


Piecewise flat Metrics on Surfaces and the Moduli Space

M. Troyanov 

2006. Teichmüller Space (Classical and Quantum), Oberwolfach, May 28th — June 3rd, 2006. p. 1602.

Sobolev inequalities for differential forms and $L_{q,p}$-cohomology

V. Gol’dshtein; M. Troyanov 

Journal of Geometric Analysis. 2006. Vol. 16, num. 4, p. 597-631. DOI : 10.1007/BF02922133.

Regularity in metric spaces

S. Timochine / M. Troyanov (Dir.)  

Lausanne, EPFL, 2006. 


Thurston’s weak metric on the Teichmüller space of the torus

A. Belkhirat; A. Papadopoulos; M. Troyanov 

Trans. Am. Math. Soc.. 2005. Vol. 357, num. 8, p. 3311-3324. DOI : 10.1090/S0002-9947-05-03735-9.


Tangent Spaces to Metric Spaces: Overview and Motivations

M. Troyanov 

Séminaire Borel 2003 (IIIème Cycle Romand de Mathématiques). , Berne,

Mean curvature and asymptotic volume of small balls

D. Hulin; M. Troyanov 

American Mathematical Monthly. 2003. Vol. 110, num. 10, p. 947-950. DOI : 10.2307/3647968.


Liouville type theorems for mappings with bounded (co)-distortion

M. Troyanov; S. Vodop’yanov 

Annales de l’Institut Fourier. 2002. Vol. 52, num. 6, p. 1753-1784. DOI : 10.5802/aif.1933.

Capacities in metric spaces

V. Gol’dshtein; M. Troyanov 

Integral Equations Oper. Theory. 2002. Vol. 44, num. 2, p. 212-242. DOI : 10.1007/BF01217533.


Boundary behavior of quasi-regular maps and the isodiametric profile

B. Hanson; P. Koskela; M. Troyanov 

Conformal Geometry and Dynamics. 2001. Vol. 5, p. 81–99. DOI : 10.1090/S1088-4173-01-00076-5.

Voronoi diagrams on piecewise flat surfaces and an application to biological growth

C. Indermitte; T. M. Liebling; M. Troyanov; H. Clémençon 

Theoretical Computer Science. 2001. Vol. 263, num. 1-2, p. 263-274. DOI : 10.1016/S0304-3975(00)00248-6.

Concentration et Inégalité de Poincaré

M. Troyanov 

Séminaire Borel 2001 (IIIème Cycle Romand de Mathématiques). , Berne,

Axiomatic theory of Sobolev spaces

V. Gol’dshtein; M. Troyanov 

Expo. Math.. 2001. Vol. 19, num. 4, p. 289-336. DOI : 10.1016/S0723-0869(01)80018-9.

An integral characterization of Hajlasz-Sobolev space

M. Troyanov; V. Gol’dshtein 

C. R. Acad. Sci. Paris Sér. I Math.. 2001. Vol. 333, num. 5, p. 445-450. DOI : 10.1016/S0764-4442(01)02088-2.


Approximately Lipschitz mappings and Sobolev mappings between metric spaces.

M. Troyanov 


Solving the $p$-Laplacian on manifolds

M. Troyanov 

Proceedings of the American Mathematical Society. 2000. Vol. 128, num. 2, p. 541-545. DOI : 10.1090/S0002-9939-99-05035-2.


Parabolicity of manifolds

M. Troyanov 

Siberian Adv. Math.. 1999. Vol. 9, num. 4, p. 125-150.

The Kelvin-Nevanlinna-Royden criterion for $p$-parabolicity

V. Gol’dshtein; M. Troyanov 

Mathematische Zeitschrift. 1999. Vol. 232, num. 4, p. 607-619. DOI : 10.1007/PL00004775.


Sur la non-résolubilité du $p$-laplacien sur $R^n$

V. Gol’dshtein; M. Troyanov 

Comptes Rendus de l’Académie des Sciences – Series I – Mathematiques. 1998. Vol. 326, num. 10, p. 1185-1187. DOI : 10.1016/S0764-4442(98)80224-3.

L’horizon de SOL

M. Troyanov 

Expo. Math.. 1998. Vol. 16, num. 5, p. 441-479.

The $L_{pq}$-cohomology of SOL

V. Gol’dshtein; M. Troyanov 

Annales de la Faculté des sciences de Toulouse : Mathématiques. 1998. Vol. 7, num. 4, p. 687-698.


Le polytechnicien est-il un universitaire ?

M. Troyanov 



Riemann surfaces with simple singularities. (Surfaces riemanniennes à singularités simples.)

M. Troyanov 



Prescribing curvature on open surfaces

D. Hulin; M. Troyanov 

Mathematische Annalen. 1992. Vol. 293, num. 1, p. 277-315. DOI : 10.1007/BF01444716.

Dialogue Polynomial

M. Troyanov 



Un principe de concentration-compacité pour les suites de surfaces riemanniennes

M. Troyanov 

Ann. Inst. H. Poincaré Anal. Non Linéaire. 1991. Vol. 8, num. 5, p. 419–441. DOI : 10.1016/S0294-1449(16)30255-4.

Prescribing curvature on compact surfaces with conical singularities

M. Troyanov 

Trans. Am. Math. Soc.. 1991. Vol. 324, num. 2, p. 793-821. DOI : 10.2307/2001742.

The Schwarz lemma for nonpositively curved Riemannian surfaces

M. Troyanov 

Manuscr. Math.. 1991. Vol. 72, num. 3, p. 251-256. DOI : 10.1007/BF02568278.


Some Universal Estimates on Eigenvalues of orientable Riemannian Surfaces.

M. Troyanov 


Espaces à courbure négative et groupes hyperboliques

M. Troyanov 

Sur les groupes hyperboliques d’après Mikhael Gromov; Boston: Birkhäuser, 1990. p. 47-66.

Sur la courbure des surfaces de Riemann ouvertes. (On the curvature of open Riemann surfaces).

D. Hulin; M. Troyanov 

C. R. Acad. Sci. Paris Sér. I Math.. 1990. Vol. 310, num. 4, p. 203-206.

Coordonnées polaires sur les surfaces riemanniennes singulières (polar coordinates on singular Riemannian surfaces)

M. Troyanov 

Annales de l’Institut Fourier. 1990. Vol. 40, num. 4, p. 913-937. DOI : 10.5802/aif.1241.


Metrics of constant curvature on a sphere with two conical singularities

M. Troyanov; F. J. Carreras; O. Gil-Medrano; A. Naveira 

1989. Third International Symposium on Differential Geometry at Peñiscola 1988, Peñiscola, June 5-12, 1988. p. 296-306. DOI : 10.1007/BFb0086431.


Les surfaces riemanniennes à singularités coniques

M. Troyanov / A. Haefliger (Dir.)  

Université de Genève, 1987. 


Les surfaces euclidiennes à singularités coniques. (Euclidean surfaces with cone singularities).

M. Troyanov 

L’Enseignement Mathématique. 1986. Vol. 32, num. 1-2, p. 79-94. DOI : 10.5169/seals-55079.