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Journal of the American Mathematical Society, ISSN 0894-0347, 04/2016, Volume 29, Issue 2, pp. 495 - 535
We study Riemann surface laminations in complex algebraic surfaces of general type. We focus on the topology and dynamics of minimal sets of holomorphic... 
Riemann surfaces laminations | Harmonic measure | Lyapunov exponent | Minimal set | Surface of general type | Levi-flat hypersurface | Thurston’s geometry | BROWNIAN-MOTION | ANOSOV-FLOWS | MATHEMATICS | BUNDLES | BOUNDARIES | FOLIATIONS | RIEMANN SURFACES | COMPLEX-SURFACES | MANIFOLDS | LEVI-FLAT | ENTROPY
Journal Article
International Journal of Mathematics, ISSN 0129-167X, 01/2020, Volume 31, Issue 1, p. 2050004
Let X be a compact connected Kähler manifold of dimension ≥ 3 and L a C ∞ Levi flat hypersurface in X . Then the normal bundle to the Levi foliation does not... 
MATHEMATICS | MINIMAL SETS | FOLIATIONS | OPERATOR | SPACES | REGULARITY | THEOREM | Levi flat hypersurface | weighted partial derivative-equation
Journal Article
Mathematische Annalen, ISSN 0025-5831, 6/2016, Volume 365, Issue 1, pp. 381 - 399
This is the first article of the two papers in which we investigate the holomorphic and formal flattening problem for a codimension two real submanifold in... 
Mathematics, general | Mathematics | SPACE | MATHEMATICS | LEVI-FLAT HYPERSURFACES | REAL SURFACES | NORMAL FORMS | CONVERGENCE | COMPLEX TANGENTS | TRANSFORMATIONS
Journal Article
Arkiv for Matematik, ISSN 0004-2080, 2018, Volume 56, Issue 2, pp. 395 - 408
It is proved that dicritical singularities of real analytic Levi-flat sets coincide with the set of Segre degenerate points. 
Levi-flat set | Foliation | Segre variety | Dicritical singularity | MATHEMATICS | dicritical singularity | HYPERSURFACES | foliation
Journal Article
Indiana University Mathematics Journal, ISSN 0022-2518, 2017, Volume 66, Issue 3, pp. 901 - 925
Journal Article
Advances in Mathematics, ISSN 0001-8708, 02/2017, Volume 308, pp. 1009 - 1073
This is the second article of the two papers, in which we investigate the holomorphic and formal flattening problem of a non-degenerate CR singular point of a... 
CR singular points | Formal flattening | Bishop invariants | Integrability condition | Nonminimal CR points | REAL SURFACES | COMPLEX TANGENTS | C2 | SPACE | MATHEMATICS | SUBMANIFOLDS | LEVI-FLAT HYPERSURFACES | NORMAL FORMS | BOUNDARY | TRANSFORMATIONS
Journal Article
Bulletin of the Australian Mathematical Society, ISSN 0004-9727, 08/2013, Volume 88, Issue 1, pp. 64 - 69
A generically embedded real submanifold of codimension two in a complex manifold has isolated complex points that can be classified as either elliptic or... 
CR manifolds | complex points | MATHEMATICS | LEVI-FLAT HYPERSURFACES
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2018, Volume 461, Issue 2, pp. 1308 - 1326
In this paper we present some linear algebra behind quadratic parts of quadratically flat complex points of codimension two real submanifold in a complex... 
Complex points | Simultaneous reduction | CR manifolds | Normal forms | MATHEMATICS, APPLIED | C-N | LOCAL HULL | REAL SURFACES | HOLOMORPHY | CONSIMILARITY | CANONICAL FORM | MATHEMATICS | LEVI-FLAT HYPERSURFACES | NONSINGULAR PENCIL | HERMITIAN MATRICES | TRANSFORMATIONS | Mathematics - Complex Variables
Journal Article
Journal für die reine und angewandte Mathematik (Crelles Journal), ISSN 0075-4102, 04/2019, Volume 2019, Issue 749, pp. 87 - 132
Kuranishi’s fundamental result (1962) associates to any compact complex manifold a finite-dimensional analytic space which has to be thought of as a local... 
MATHEMATICS | COMPLEX | FAMILIES | DEFORMATIONS | Mathematics - Complex Variables
Journal Article
Journal of Geometric Analysis, ISSN 1050-6926, 04/2018, Volume 28, Issue 2, pp. 1728 - 1748
We study bounded pseudoconvex domains in 2-dimensional complex Euclidean spaces. We are interested in developing sufficient and necessary conditions for the... 
Plurisubharmonicity | Diederich–Fornæss index | Levi-flat sets | Necessary conditions | MATHEMATICS | Diederich-Fornaess index | PLURISUBHARMONIC DEFINING FUNCTIONS | VECTOR-FIELDS | MANIFOLDS
Journal Article
The Journal of Geometric Analysis, ISSN 1050-6926, 4/2019, Volume 29, Issue 2, pp. 1407 - 1427
An irreducible real analytic subvariety H of real dimension $$2n +1$$ 2 n + 1 in a complex manifold M is a Levi-flat subset if its regular part carries a... 
Abstract Harmonic Analysis | Primary 32S65 | Fourier Analysis | Secondary 32V40 | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Holomorphic foliations | Mathematics | Differential Geometry | Dynamical Systems and Ergodic Theory | CR-manifolds | Levi-flat varieties | MATHEMATICS | SINGULARITIES | HYPERSURFACES
Journal Article
Geometriae Dedicata, ISSN 0046-5755, 10/2018, Volume 196, Issue 1, pp. 35 - 44
We study holomorphic foliations tangent to singular real-analytic Levi-flat hypersurfaces in compact complex manifolds of complex dimension two. We give some... 
Levi-flat hypersurfaces | Primary 32V40 | 32S65 | Convex and Discrete Geometry | Algebraic Geometry | Holomorphic foliations | Mathematics | Hyperbolic Geometry | Dicritical singularities | Projective Geometry | Topology | Differential Geometry | MATHEMATICS | NORMAL FORMS | Mathematics - Complex Variables
Journal Article
Izvestiya Mathematics, ISSN 1064-5632, 2017, Volume 81, Issue 5, pp. 1030 - 1043
We establish an effective criterion for a dicritical singularity of a real analytic Levi-flat hypersurface. The criterion is stated in terms of Segre... 
Levi-flat set | Foliation | Current | Dicritical singularity | MATHEMATICS | current | FOLIATIONS | dicritical singularity | foliation | Singularities | Hyperspaces | Criteria
Journal Article
Bollettino dell'Unione Matematica Italiana, ISSN 1972-6724, 3/2019, Volume 12, Issue 1, pp. 197 - 219
In order to study the deformations of foliations of codimension 1 of a smooth manifold L, de Bartolomeis and Iordan defined the DGLA $$ \mathcal {Z}^{*}\left(... 
32E99 | 53C12 | Differential graded Lie Algebras | Levi flat hypersurface | Mathematics, general | 16W25 | Mathematics | Foliations | Maurer–Cartan equation | Primary 32G10 | Graded derivations
Journal Article
Annales de l'Institut Fourier, ISSN 0373-0956, 2017, Volume 67, Issue 6, pp. 2426 - 2462
Journal Article
Commentarii Mathematici Helvetici, ISSN 0010-2571, 2015, Volume 90, Issue 2, pp. 479 - 502
It is shown that the Levi foliation of a real analytic Levi-flat hypersurface extends to a $d$-web near a nondicritical singular point and admits a... 
Several complex variables and analytic spaces | Ordinary differential equations | Dynamical systems and ergodic theory | Levi-flat hypersurfaces | Foliations | Webs | MATHEMATICS | webs | foliations
Journal Article
Journal of Geometric Analysis, ISSN 1050-6926, 04/2018, Volume 28, Issue 2, pp. 1052 - 1077
We give local criteria for smooth non-embeddability of Levi-flat manifolds. For this purpose, we pose an analogue of Ueda theory on the neighborhood structure... 
Pseudo-flat neighborhoods | Ueda theory | Levi-flat manifolds | MATHEMATICS | MINIMAL SETS | NONEXISTENCE | FOLIATIONS | HYPERSURFACES | CURVATURE | COMPLEX PROJECTIVE SPACES | SURFACES
Journal Article
The Journal of Geometric Analysis, ISSN 1050-6926, 7/2019, Volume 29, Issue 3, pp. 2776 - 2804
Journal Article
Kyushu Journal of Mathematics, ISSN 1340-6116, 2012, Volume 66, Issue 2, pp. 375 - 381
For a real hypersurface M of class C2 in Cn , n ≥ 2, an explicit formula for the Levi form of the distance function δM to M is given in terms of the Hermitian... 
distance | strictly plurisubharmonic | Levi form | Levi-flat | Strictly plurisubharmonic | Distance
Journal Article
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