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Viet Anh Nguyen

Professeur des universités CNU : SECTION 25 - MATHEMATIQUES

Research

Recent Preprints/Publications

 

Selected Publications

        With T.-C. Dinh and N. Sibony. Duke. Math. J., 171(13): 2627-2698 (15 September 2022). DOI: 10.1215/00127094-2022-0044, 72 pages.

 

Research Works

Preprints

  1. Positive plurisubharmonic currents: generalized Lelong numbers and tangent theorems.
    (2021), version 2, 241 pages, available at [preprint]
  2. Singular holomorphic foliations by curves II: Negative Lyapunov exponent.
    (2018), version 2, 42 pages, available at [preprint]

Accepted articles

  1.  Holomorphic sections of line bundles vanishing along subvarieties.
    With D. Coman and G. Marinescu. (2022),  Indiana Univ. Math. J.,  35 pages, (to appear).
  2. Singular holomorphic foliations by curves. III: Zero Lelong numbers.
    Math. Ann.  (2020), version 2, 35 pages, (to appear).

Articles

2022

  1. Unique ergodicity for foliations on compact Kähler surfaces. 

        With T.-C. Dinh and N. Sibony. Duke. Math. J., 171(13): 2627-2698 (15 September 2022). DOI: 10.1215/00127094-2022-0044, 72 pages.

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.
    Dedicated to My Beloved Father. [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.
    Dedicated to the memory of Professor Gennadi M. Henkin. [article|preprint]
  3. Ergodic theory for Riemann surface laminations: a survey.
    In: 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.
    Dedicated to Professor Kang-Tae Kim for his sixtieth birthday. [article|preprint]

2018

  1. 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.
    Dedicated to Professor Lê Tuân Hoa on the occasion of his sixtieth birthday. [article|preprint]
  2. Approximation and equidistribution results for pseudo-effective line bundles.
    With D. Coman and G. Marinescu. J. Math. Pures Appl. (9), 115 (2018), 218–236. [article|preprint]
  3. Large deviations principle for some beta-ensembles.
    With T.-C. Dinh. Trans. Amer. Math. Soc., 370 (2018), no. 9, 6565–6584. [article|preprint]
  4. Singular holomorphic foliations by curves I: Integrability of holonomy cocycle in dimension 2.
    Invent. Math. 212 (2018), no. 2, 531–618.
    Dedicated to Professor Nessim Sibony for his seventieth birthday. [article|preprint]
  5. 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.

     With T.-C. Dinh and T.-T. Truong. Bull. Lond. Math. Soc. 49 (2017), no. 6, 947–964.

      Dedicated to Professor Ngô Viêt Trung. [article|preprint]

  1. On the asymptotic behavior of Bergman kernels for positive line bundles.

      With T.-C. Dinh and X.-N. Ma. Pacific J. Math. 289 (2017), no. 1, 71–89. [article|preprint]

  1. Equidistribution speed for Fekete points associated with an ample line bundle.

     With T.-C. Dinh and X.-N. Ma. Ann. Sci. Éc. Norm. Supér. (4) 50 (2017), no. 3, 545–578. [article|preprint]

  1. 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.
    With D. Coman and 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.
    With T.-C. Dinh and 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.
    With T.-C. Dinh. J. Funct. Anal., 266, (2014), no. 1, 67–84. [article]
  2. Entropy for hyperbolic Riemann surface laminations II.
    With T.-C. Dinh and 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.
    With T.-C. Dinh and 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.
    With 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.
    With T.-C. Dinh and T.-T. Truong. Commun. Contemp. Math., 14, (2012), no. 6, 18 pages. [article|preprint]
  2. Heat equation and ergodic theorems for Riemann surface laminations.
    With T.-C. Dinh and 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.
    With T.-C. Dinh. Comment. Math. Helv. 86, (2011), no. 4, 817–840. [article|preprint]

2010

  1. Exponential estimates for plurisubharmonic functions and stochastic dynamics.
    With T.-C. Dinh and 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]
    The proof of the main result of the article is incomplete.
    A complete proof has been announced here:
    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]
    A detailed complete proof has been posted here:
    Corrigendum: Conical plurisubharmonic measure and new cross theorems.
    17 pages, available at [preprint]
  3. Cross theorems with singularities.
    With P. Pflug. J. Geom. Anal. 20 (2010), no. 1, 193-218. [article|preprint]

2009

  1. Recent developments in the theory of separately holomorphic mappings.
    (Survey article) Colloq. Math. 117 (2009), no. 2, 175-206. [article|preprint]
  2. Boundary cross theorem in dimension 1 with singularities.                                                  

      With P. Pflug. Indiana Univ. Math. J. 58 (2009), no. 1, 393-414. [article|preprint]

2008

  1. Dynamics of horizontal-like maps in higher dimensions.
    With T.-C. Dinh and 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.
    With P. Pflug. Arch. Math. (Basel) 89 (2007), no. 4, 326-338. [article|preprint]
  2. On thermodynamics of rational maps on the Riemann sphere.
    With T.-C. Dinh and N. Sibony. Ergodic Theory Dyn. Syst. 27 (2007), no. 4, 1095-1109. [article|preprint]
  3. Generalization of a theorem of Gonchar.
    With P. Pflug. Ark. Mat. 45 (2007), no. 1, 105-122. [article|preprint]
  4. Boundary cross theorem in dimension 1

       With 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.
    With T.-C. Dinh. Geom. Funct. Anal. 16 (2006), no. 4, 838-849. [article|preprint]
  2. Algebraic degrees for iterates of meromorphic self-maps of  <nobr aria-hidden="true">Pk</nobr>.
    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.
    With 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.
    With 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.

      With 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

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

 

Theses

  • Holomorphie séparée, Dynamique complexe et Théorèmes de Hodge--Riemann.
    Habilitation à diriger des recherches defended at the Université Paris-Sud XI (Orsay, France) on 25 June 2007.
    [Abstract|Full text]
  • Problème de Lu Qi-Keng, Théorie Hp et Équation de Cauchy-Riemann.

       Ph.D Thesis defended at the Université d'Aix-Marseille I (Marseille, France) on 6 March 2001.
[Abstract|Full text]