Viêt Anh NGUYÊN: Research Works

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### Preprints

1. Distribution of scattering resonances for generic Schrödinger operators.
With T.-C. Dinh. (2017), 19 pages, available at [preprint]

### Accepted articles

1. Super-potentials, densities of currents and number of periodic points for holomorphic maps.
With T.-C. Dinh and 34 pages, available at [preprint].
Dedicated to Professor Lê Tuân Hoa on the occasion of his sixtieth birthday.

2. Ergodic theory for Riemann surface laminations: a survey.
(Survey article) Geometric Complex Analysis, (2018), 31 pages, available at [preprint].
Dedicated to Professor Kang-Tae Kim for his sixtieth birthday.

### 2018

1. Geometric characterization of Lyapunov exponents for Riemann surface laminations.
J. Geom. Anal., https://doi.org/10.1007/s12220-017-9919-8, (2018), 37 pages.
Dedicated to the memory of Professor Gennadi M. Henkin.
2. Large deviations principle for some beta-ensembles.
With T.-C. Dinh. Trans. Amer. Math. Soc., https://doi.org/10.1090/tran/7171, (2018), 20 pages.
3. Directed harmonic currents near hyperbolic singularities.
Ergodic Theory Dyn. Syst., https://doi.org/10.1017/etds.2017.2, (2018), 18 pages.
4. Approximation and equidistribution results for pseudo-effective line bundles.
With D. Coman and J. Math. Pures Appl. (9), 115 (2018), 218–236.
5. 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.
6. ### 2017

7. 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.
8. On the asymptotic behavior of Bergman kernels for positive line bundles.
With T.-C. Dinh and . Pacific J. Math. 289 (2017), no. 1, 71–89.
9. Equidistribution speed for Fekete points associated with an ample line bundle.
With T.-C. Dinh and . Ann. Sci. Éc. Norm. Supér. (4) 50 (2017), no. 3, 545–578.
10. Oseledec multiplicative ergodic theorems for laminations.
vol. 246, no. 1164, Amer. Math. Soc., Providence, RI, 2017, pp. 1–174.

### 2016

1. Hölder singular metrics on big line bundles and equidistribution.
With D. Coman and . Int. Math. Res. Not. IMRN, 2016, (2016), no. 16, 5048–5075.

### 2015

1. Equidistribution for meromorphic maps with dominant topological degree.
With T.-C. Dinh and Indiana Univ. Math. J.,64, (2015), no. 6, 1805–1828.

### 2014

1. Characterization of Monge-Ampère measures with Hölder continuous potentials.
With J. Funct. Anal., 266, (2014), no. 1, 67–84.
2. Entropy for hyperbolic Riemann surface laminations II.
With T.-C. Dinh and 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 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 Illinois J. Math., 57, (2013), no. 1, 121–144.

### 2012

1. On the dynamical degrees of meromorphic maps preserving a fibration.
With T.-C. Dinh and Commun. Contemp. Math., 14, (2012), no. 6, 18 pages.
2. Heat equation and ergodic theorems for Riemann surface laminations.
With T.-C. Dinh and Math. Ann., 354, (2012), no. 1, 331–376.
3. Green currents for quasi-algebraically stable meromorphic self-maps of $\mathbb{P}^k$.
Publ. Math., 56, (2012), no. 1, 127–146.

### 2011

1. Comparison of dynamical degrees for semi-conjugate meromorphic maps.
With Comment. Math. Helv. 86, (2011), no. 4, 817–840.

### 2010

1. Exponential estimates for plurisubharmonic functions and stochastic dynamics.
With T.-C. Dinh and J. Differential Geom. 84 (2010), no. 3, 465-488.
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 J. Geom. Anal. 20 (2010), no. 1, 193-218.

### 2009

1. Recent developments in the theory of separately holomorphic mappings.
(Survey article) Colloq. Math. 117 (2009), no. 2, 175-206.
2. Boundary cross theorem in dimension $1$ with singularities.
With Indiana Univ. Math. J. 58 (2009), no. 1, 393-414.

### 2008

1. Dynamics of horizontal-like maps in higher dimensions.
With T.-C. Dinh and Adv. Math. 219 (2008), no. 5, 1689-1721.
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.

### 2007

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

### 2006

1. The mixed Hodge-Riemann bilinear relations for compact Kähler manifolds.
With Geom. Funct. Anal. 16 (2006), no. 4, 838-849.
2. Algebraic degrees for iterates of meromorphic self-maps of $\mathbb{P}^k$.
Publ. Math. 50 (2006), no. 2, 457-473.

### 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.

### 2004

1. A boundary cross theorem for separately holomorphic functions.
With Ann. Polon. Math. 84 (2004), no. 3, 237-271.

### 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 Ann. Polon. Math. 82 (2003), no. 2, 171-187.
3. Optimal Lipschitz estimates for the $\overline\partial$-equation on a class of convex domains.
With Ann. Fac. Sci. Toulouse (6) 12 (2003), no. 2, 179-243.

### 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 $\overline\partial$ dans une classe de domaines convexes.
With C. R. Acad. Sci. Paris Sér. I Math. 332 (2001), no. 12, 1065-1070. [article]
2. Lipschitz estimates for the $\overline\partial$-equation on the minimall balls.
With 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 $\mathbb{C}^n$ ($n\geq 3$).
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.
• Problème de Lu Qi-Keng, Théorie $H^p$ et Équation de Cauchy-Riemann.
Ph.D Thesis defended at the Université d'Aix-Marseille I (Marseille, France) on 6 March 2001.

Département de Mathématiques, Cité Scientifique - Bâtiment M2, F-59655 VILLENEUVE D'ASCQ, France
Tél : +33 (0) 3 20 43 42 34