Research

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

[18] Extremal discs and Segre varieties for real-analytic hypersurfaces in C^2 (with G. Della Sala and B. Lamel)
Submitted for publication.

[17] Jet determination of smooth CR automorphisms and generalized stationary discs (with G. Della Sala and B. Lamel)
To appear in Mathematische Zeitschrift .

[16] Extremal and stationary discs for the Kobayashi k-metric (with G. Della Sala and J.-C. Joo)
To appear in Michigan Mathematical Journal.

[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 the 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 Journal of 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 the 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



Events organization

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"