Real analytic maximum modulus manifolds in strictly pseudoconvex boundaries
Real equivalence of complex matrix pencils and complex projections of real Segre varieties.
Real hypersurfaces in complex two-plane Grassmannians with certain commuting condition II
Lee, Kim and Suh (2012) gave a characterization for real hypersurfaces of Type in complex two plane Grassmannians with a commuting condition between the shape operator and the structure tensors and for in . Motivated by this geometrical notion, in this paper we consider a new commuting condition in relation to the shape operator and a new operator induced by two structure tensors and . That is, this commuting shape operator is given by . Using this condition, we prove that...
Régularité hölderienne du ...b dans les hypersurfaces 1-convexes-concaves.
Regularity and extremality of quasiconformal homeomorphisms on CR 3-manifolds.
Regularity of CR Mappings.
Regularity of local embeddings of strictly pseudoconvex CR structures.
Regularity of the tangential Cauchy-Riemann complex and applications
Résolution du pour les courants prolongeables définis dans un anneau
Rigidity of CR morphisms between compact strongly pseudoconvex CR manifolds
Let and be two compact strongly pseudoconvex CR manifolds of dimension which bound complex varieties and with only isolated normal singularities in and respectively. Let and be the singular sets of and respectively and is nonempty. If and the cardinality of is less than 2 times the cardinality of , then we prove that any non-constant CR morphism from to is necessarily a CR biholomorphism. On the other hand, let be a compact strongly pseudoconvex CR manifold of...
Rigidity of CR submanifolds and analyticity of CR immersions.
Segre Families and Real Hypersurfaces.
Semi-global solutions of ∂b with Lp (1 ≤ p ≤ ∞) bounds on strongly pseudoconvex real hypersurfaces in Cn (n ≥ 3).
Let M be an open subset of a compact strongly pseudoconvex hypersurface {ρ = 0} defined by M = D × Cn-m ∩ {ρ = 0}, where 1 ≤ m ≤ n-2, D = {σ(z1, ..., zm) < 0} ⊂ Cm is strongly pseudoconvex in Cm. For ∂b closed (0, q) forms f on M, we prove the semi-global existence theorem for ∂b if 1 ≤ q ≤ n-m-2, or if q = n - m - 1 and f satisfies an additional “moment condition”. Most importantly, the solution operator satisfies Lp estimates for 1 ≤ p ≤ ∞ with p = 1 and ∞ included.
Singular Levi-flat hypersurfaces and codimension one foliations
We study Levi-flat real analytic hypersurfaces with singularities. We prove that the Levi foliation on the regular part of the hypersurface can be holomorphically extended, in a suitable sense, to neighbourhoods of singular points.
Smooth, but not Complex-Analytic Pluripolar Sets.
Smoothness of Cauchy Riemann maps for a class of real hypersurfaces.
We study the regularity problem for Cauchy Riemann maps between hypersurfaces in Cn. We prove that a continuous Cauchy Riemann map between two smooth C∞ pseudoconvex decoupled hypersurfaces of finite D'Angelo type is of class C∞.
Solvable Lie algebras and the embedding of CR manifolds
In questo lavoro si dà un criterio sufficiente per l'immersione di una varietà CR astratta di codimensione arbitraria in una di codimensione CR più bassa. La condizione trovata è necessaria per l'immersione in una varietà complessa (codimensione CR uguale a zero). Essa è formulata in termini dell'esistenza di una sottoalgebra di Lie di campi di vettori complessi trasversale alla distribuzione di Cauchy-Riemann.
Some applications of Cartain's theory on three-dimensional Cauchy-Riemann geometry.
Some applications of Cauchy-Fantappie forms to (local) problems on
Some remarks concerning holomorphically convex hulls and envelopes of holomorphy.