My research works are focused on the field of Several Complex Variables, a theme at the intersection between Analysis, Partial Differential Equations and Geometry. Two essential groups of questions arise in my works. The first framework concerns complex and differential geometry considerations relying on sharp analysis on manifolds such as local and global properties of solutions of nonlinear elliptic PDE systems or sharp estimates of invariant metrics. The second one is centered on analytic aspects of the theory such as boundary value problems, potential theory or extension properties.

Papers

[26] On the envelope of Poisson functional on almost complex manifolds (with U. Kuzman)
Submitted for publication.

[25] A sphericity criterion for strictly pseudoconvex hypersurfaces in C^2 via invariant curves (with G. Della Sala and B. Lamel)
Accepted for publication in Revista Matemática Iberoamericana.

[24] Extremal discs and Segre varieties for real-analytic hypersurfaces in C^2 (with G. Della Sala and B. Lamel)
To appear in Proceedings of the AMS.

[23] On the higher order Kobayashi pseudometric (with S. Ban, A. Jaber Chehayeb, A. Salha and W. Tabbara)
Published in Complex Variables and Elliptic Equations, Volume 69, 2024, 1935–1948. This work was done in the framework of the Summer Research Camp in Mathematics.

[22] Explicit construction of stationary discs and its consequences for nondegenerate quadrics (with F. Meylan)
Published in Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, Volume 24, 2023, 1875-1892.

[21] The 1-jet determination of stationary discs attached to generic CR submanifolds (with F. Meylan)
Published in Complex Analysis and its Synergies, Volume 8, 2022, No. 3, 7 pp. Special issue “Mappings and symmetry in complex and CR geometry”.

[20] Nondefective stationary discs and 2-jet determination in higher codimension (with F. Meylan)
Published in Journal of Geometric Analysis, Volume 31, 2021, 6292-6306.

[19] Addendum to “Stationary discs and finite jet determination for non-degenerate generic real submanifolds” (with L. Blanc-Centi and F. Meylan)
Published in Advances in Mathematics, Volume 383, 2021, Paper No. 107701, 3 pp.

[18] The stationary disc method in the unique jet determination of CR automorphisms
Published in Complex Analysis and its Synergies, Volume 6, 2020, Paper No. 8, 12 pp.
This is part of the topical collection Geometric Analysis of Partial Differential Equations and Several Complex Variables: In Honor of Nick Hanges.

[17] Extremal and stationary discs for the Kobayashi k-metric (with G. Della Sala and J.-C. Joo)
Published in Michigan Mathematical Journal, Volume 69, 2020, 451-463.

[16] Jet determination of smooth CR automorphisms and generalized stationary discs (with G. Della Sala and B. Lamel)
Published in Mathematische Zeitschrift, Volume 294, 2020, 1611-1634.

[15] Riemann-Hilbert problems with constraints (with G. Della Sala)
Published in the Proceedings of the AMS, Volume 147, 2019, 2123-2131.

[14] Stationary discs and finite jet determination for non-degenerate generic real submanifolds (with L. Blanc-Centi and F. Meylan)
Published in Advances in Mathematics, Volume 343, 2019, 910-934.

[13] The star function for meromorphic functions of several complex variables (with F. Abi-Khuzam and G. Della Sala)
Published in Complex Variables and Elliptic Equations, Volume 64, 2019, 26-39.

[12] Invariant holomorphic discs in some non-convex domains (with H.Gaussier)
Published in Proceedings of the AMS, Volume 146, 2018, 1197-1205.

[11] Local approximation of non-holomorphic discs in almost complex manifolds (with U. Kuzman)
Published in Mathematical Analysis and Applications, Volume 458, 2018, 123-133.

[10] Stationary discs for smooth hypersurfaces of finite type and finite jet determination (with G. Della Sala)
Published in Journal of Geometric Analysis , Volume 25, 2015, 2516-2545.

[9] Gromov hyperbolicity of strongly pseudoconvex almost complex manifolds (with H. Gaussier)
Published in Proceedings of the AMS, Volume 143, 2015, 3901–3913.

[8] Quasi-isometries in strongly convex domains (with H. Gaussier)
Published in Journal of Mathematical Analysis and Applications, Volume 420, 2014, 873-877.

[7] Common boundary values of holomorphic functions for two-sided complex structures (with X. Gong and J.-P. Rosay)
Published in Michigan Mathematical Journal , Volume 63, 2014, 239-332.

[6] Stationary holomorphic discs and finite jet determination problems (with L. Blanc-Centi)
Published in Mathematische Annalen, Volume 358, 2014, 477-509

[5] Dirichlet and Neumann problems for planar domains with parameter (with X. Gong)
Published in Transactions of the AMS, Volume 366, 2014, 159-217

[4] A note on the geometry of pseudoconvex domains of finite type in almost complex manifolds
Published in Proceedings of the AMS, Volume 140, 2012, 1633-1641

[3] Pseudoconvex domains of finite D’Angelo type in almost complex manifolds of dimension four
Published in Mathematische Zeitschrift, Volume 264, 2010, 423-457

[2] Sharp estimates of the Kobayashi metric and Gromov hyperbolicity
Published in Journal of Mathematical Analysis and Applications, Volume 345, 2008, 825-844

[1] Almost complex structures on the cotangent bundle
Published in Complex Variables and Elliptic Equations, Volume 52, 2007, 741-754

Event Organization

June 2023: CIMPA School on Complex Analysis and Geometry at CAMS and the Department of Mathematics at AUB, Beirut, Lebanon.
May 2017: Conference on Complex Geometry and PDEs at CAMS and the Department of Mathematics at AUB, Beirut, Lebanon.
May 2016: Conference on Differential Geometry at CAMS and the Department of Mathematics at AUB, Beirut, Lebanon.
March 2015: Graduate minicourse: Hervé Gaussier (University of Grenoble, France) at CAMS, AUB.
2014-2016: Organizer of the Analysis and Geometry Seminar at the Department of Mathematics, AUB.
November 2014: Conference on Partial Differential Equations in Complex Geometry and Singular Spaces at CAMS, Beirut, Lebanon.
2013-2014: Co-organizer (with G. Della Sala) of the Complex Analysis Seminar at the University of Vienna, Austria.

PhD Thesis

Here is a copy of my PhD thesis “Local Analysis on Almost Complex Manifolds”