Prépublications

1. Positive plurisubharmonic currents: generalized Lelong numbers and tangent theorems.
   (2021), version 2, 241 pages, disponible au [preprint]
2. Restricted spaces of holomorphic sections vanishing along subvarieties.
   Avec D. Coman et G. Marinescu. (2023),  22 pages, disponible au [preprint]

À paraître

1. Holomorphic sections of line bundles vanishing along subvarieties.
   Avec D. Coman et G. Marinescu.  Indiana Univ. Math. J., (2022),   35 pages, (à paraître).
2. Singular holomorphic foliations by curves. III: Zero Lelong numbers.
   Math. Ann.  (2023),  39 pages,  DOI: doi.org/10.1007/s00208-023-02618-6

Articles

2023  

1. Singular holomorphic foliations by curves II: Negative Lyapunov exponent

        J. Geom. Anal. 33 (2023), no. 10, Paper No. 315, 53 pp.

2022   

1.  Unique ergodicity for foliations on compact Kähler surfaces. 

      Avec T.-C. Dinh et N. Sibony. Duke. Math. J. 171 (2022), no. 13, 2627–2698.

2021

1. Ergodic theorems for laminations and foliations: recent results and perspectives.
   Acta Math. Vietnam., 46 (2021), no. 1, 9–101.
   VIASM Annual Meeting, août 2019, Hanoi, Vietnam.
   Dédié à mon cher père. [article|preprint]

2020

1. Distribution of scattering resonances for generic Schrödinger operators.
   With T.-C. Dinh. J. Funct. Anal., 278 (2020), no. 10, 108446, 26 pages.
   [article|preprint]
2. Geometric characterization of Lyapunov exponents for Riemann surface laminations.
   J. Geom. Anal., 30 (2020), 2442–2478.
   Dédié en hommage au Professeur Gennadi M. Henkin. [article|preprint]

2018

1. Ergodic theory for Riemann surface laminations: a survey.
   Dans: Byun J., Cho H., Kim S., Lee KH., Park JD. (eds) Geometric Complex Analysis.
   Springer Proc. Math. Stat. vol 246. Springer, Singapore (2018), 291–327.
   Dédié au Professeur Kang-Tae Kim à l'occasion de son 60ième anniversaire. [article|preprint]
2. Super-potentials, densities of currents and number of periodic points for holomorphic maps.
   With T.-C. Dinh and D.-V. Vu. Adv. Math., 331 (2018), 874–907.
   Dédié au Professeur Lê Tuân Hoa à l'occasion de son 60ième anniversaire. [article|preprint]
3. Approximation and equidistribution results for pseudo-effective line bundles.
   Avec D. Coman et G. Marinescu. J. Math. Pures Appl. (9), 115 (2018), 218–236. [article|preprint]
4. Large deviations principle for some beta-ensembles.
   Avec T.-C. Dinh. Trans. Amer. Math. Soc., 370 (2018), no. 9, 6565–6584. [article|preprint]
5. Singular holomorphic foliations by curves I: Integrability of holonomy cocycle in dimension 2.
   Invent. Math. 212 (2018), no. 2, 531–618.
   Dédié au Professeur Nessim Sibony à l'occasion de son 70ième anniversaire. [article|preprint]
6. Directed harmonic currents near hyperbolic singularities.
   Ergodic Theory Dyn. Syst., 38 (2018), 3170–3187. [article|preprint]

2017

1. Growth of the number of periodic points for meromorphic maps.
   Avec T.-C. Dinh et T.-T. Truong. Bull. Lond. Math. Soc. 49 (2017), no. 6, 947–964.
   Dédié au Professeur Ngô Viêt Trung. [article|preprint]
2. On the asymptotic behavior of Bergman kernels for positive line bundles.
   Avec T.-C. Dinh et X.-N. Ma. Pacific J. Math. 289 (2017), no. 1, 71–89. [article|preprint]
3. Equidistribution speed for Fekete points associated with an ample line bundle.
   Avec T.-C. Dinh et X.-N. Ma. Ann. Sci. Éc. Norm. Supér. (4) 50 (2017), no. 3, 545–578. [article|preprint]
4. Oseledec multiplicative ergodic theorems for laminations.
   Memoirs of the AMS vol. 246, no. 1164, Amer. Math. Soc., Providence, RI, 2017, pp. 1–174. [article|preprint]

2016

1. Hölder singular metrics on big line bundles and equidistribution.
   Avec D. Coman et G. Marinescu. Int. Math. Res. Not. IMRN, 2016, (2016), no. 16, 5048–5075. [article|preprint]

2015

1. Equidistribution for meromorphic maps with dominant topological degree.
   Avec T.-C. Dinh et T.-T. Truong. Indiana Univ. Math. J.,64, (2015), no. 6, 1805–1828. [article|preprint]

2014

1. Characterization of Monge-Ampère measures with Hölder continuous potentials.
   Avec T.-C. Dinh. J. Funct. Anal., 266, (2014), no. 1, 67–84. [article]
2. Entropy for hyperbolic Riemann surface laminations II.
   Avec T.-C. Dinh et N. Sibony. Frontiers in Complex Dynamics: a volume in honor of John Milnor's 80th birthday, (A. Bonifant, M. Lyubich, S. Sutherland, editors), (2014), 593–622, Princeton University Press, [preprint]
3. Entropy for hyperbolic Riemann surface laminations I.
   Avec T.-C. Dinh et N. Sibony. Frontiers in Complex Dynamics: a volume in honor of John Milnor's 80th birthday, (A. Bonifant, M. Lyubich, S. Sutherland, editors), (2014), 569–592, Princeton University Press, [preprint]

2013

1. On the Lefschetz and Hodge-Riemann theorems.
   Avec T.-C. Dinh. Illinois J. Math., 57, (2013), no. 1, 121–144. [article]

2012

1. On the dynamical degrees of meromorphic maps preserving a fibration.
   Avec T.-C. Dinh et T.-T. Truong. Commun. Contemp. Math., 14, (2012), no. 6, 18 pages. [article|preprint]
2. Heat equation and ergodic theorems for Riemann surface laminations.
   Avec T.-C. Dinh et N. Sibony. Math. Ann., 354, (2012), no. 1, 331–376. [article|preprint]
3. Green currents for quasi-algebraically stable meromorphic self-maps of Pk.   Publ. Math., 56, (2012), no. 1, 127–146. [article|preprint]

2011

1. Comparison of dynamical degrees for semi-conjugate meromorphic maps.
   Avec T.-C. Dinh. Comment. Math. Helv. 86, (2011), no. 4, 817–840. [article|preprint]

2010

1. Exponential estimates for plurisubharmonic functions and stochastic dynamics.
   Avec T.-C. Dinh et N. Sibony. J. Differential Geom. 84 (2010), no. 3, 465-488. [article|preprint]
2. Conical plurisubharmonic measure and new cross theorems.
   J. Math. Anal. Appl. 365 (2010), no. 2, 429-434. [article]
   La preuve du résultat principal de cet article contient une erreur.
   Une preuve correcte est annoncée ici:
   Corrigendum to ``Conical plurisubharmonic measure and new cross theorems" [ J. Math. Anal. Appl. 365 (2010), no. 2, 429-434].
   J. Math. Anal. Appl. 403 (2013), no. 1, 330. [article]
   La preuve correcte et détaillée est mise en ligne ici:
   Corrigendum: Conical plurisubharmonic measure and new cross theorems.
   17 pages, disponible au [preprint]
3. Cross theorems with singularities.
   Avec P. Pflug. J. Geom. Anal. 20 (2010), no. 1, 193-218. [article|preprint]

2009

1. Recent developments in the theory of separately holomorphic mappings.
   (Article de survol) Colloq. Math. 117 (2009), no. 2, 175-206. [article|preprint]
2. Boundary cross theorem in dimension 1 with singularities
   Avec P. Pflug. Indiana Univ. Math. J. 58 (2009), no. 1, 393-414. [article|preprint]

2008

1. Dynamics of horizontal-like maps in higher dimensions.
   Avec T.-C. Dinh et N. Sibony. Adv. Math. 219 (2008), no. 5, 1689-1721. [article|preprint]
2. A unified approach to the theory of separately holomorphic mappings.
   Ann. Scuola Norm. Sup. Pisa Cl. Sci. serie V, 7 (2008), no. 2, 181-240. [article|preprint]

2007

1. Envelope of holomorphy for boundary cross sets.
   Avec P. Pflug. Arch. Math. (Basel) 89 (2007), no. 4, 326-338. [article|preprint]
2. On thermodynamics of rational maps on the Riemann sphere.
   Avec T.-C. Dinh et N. Sibony. Ergodic Theory Dyn. Syst. 27 (2007), no. 4, 1095-1109. [article|preprint]
3. Generalization of a theorem of Gonchar.
   Avec P. Pflug. Ark. Mat. 45 (2007), no. 1, 105-122. [article|preprint]
4. Boundary cross theorem in dimension 1.. Avec P. Pflug. Ann. Polon. Math. 90 (2007), no. 2, 149-192. [article|preprint]

2006

1. The mixed Hodge-Riemann bilinear relations for compact Kähler manifolds.
   Avec T.-C. Dinh. Geom. Funct. Anal. 16 (2006), no. 4, 838-849. [article|preprint]
2. Algebraic degrees for iterates of meromorphic self-maps of Pk..
   Publ. Math. 50 (2006), no. 2, 457-473. [article|preprint]

2005

1. A general version of the Hartogs extension theorem for separately holomorphic mappings between complex analytic spaces.
   Ann. Scuola Norm. Sup. Pisa Cl. Sci. serie V, 4 (2005), no. 2, 219-254. [article|preprint]

2004

1. A boundary cross theorem for separately holomorphic functions.
   Avec P. Pflug. Ann. Polon. Math. 84 (2004), no. 3, 237-271. [article|preprint]

2003

1. A remark on a question of Lempert-Henkin.
   Int. J. of Math. 14 (2003), no. 10, 1091-1095. [article]
2. Extension theorems of Sakai type for separately holomorphic and meromorphic functions.
   Avec P. Pflug. Ann. Polon. Math. 82 (2003), no. 2, 171-187. [article|preprint]
3. Optimal Lipschitz estimates for the ∂¯-equation on a class of convex domains.
   Avec E.-H. Youssfi. Ann. Fac. Sci. Toulouse (6) 12 (2003), no. 2, 179-243. [article|preprint]

2002

1. Fatou and Korányi-Vági type theorems on the minimal balls.
   Publ. Mat. 46 (2002), no. 1, 49-75. [article]

2001

• Estimations Lipschitziennes optimales pour l'équation ∂¯dans une classe de domaines convexes.
  Avec E.-H. Youssfi. C. R. Acad. Sci. Paris Sér. I Math. 332 (2001), no. 12, 1065-1070. [article]
•  Lipschitz estimates for the ∂¯-equation on the minimall balls.

      Avec E.-H. Youssfi. Michigan Math. J. 49 (2001), no. 2, 299-323. [article]

2000

1. The Lu Qi-Keng conjecture fails for strongly convex algebraic complete Reinhardt domains in Cn (n≥3).
   Proc. Amer. Math. Soc. 128 (2000), no. 6, 1729-1732. [article]

Mémoires

• Holomorphie séparée, Dynamique complexe et Théorèmes de Hodge--Riemann.
  Habilitation à diriger des recherches soutenue à l'Université Paris-Sud XI (Orsay, France) le 25 juin 2007.
  [le résumé|le texte]

• Problème de Lu Qi-Keng, Théorie Hp et Équation de Cauchy-Riemann.

      Thèse de doctorat soutenue à l'Université d'Aix-Marseille I (Marseille, France) le 6 mars 2001. [le résumé|le texte]