Quasiconformality of pseudo-conformal transformations and deformations of hypersurfaces in C...
Real analytic manifolds in with parabolic complex tangents along a submanifold of codimension one
We will classify -dimensional real submanifolds in which have a set of parabolic complex tangents of real dimension . All such submanifolds are equivalent under formal biholomorphisms. We will show that the equivalence classes under convergent local biholomorphisms form a moduli space of infinite dimension. We will also show that there exists an -dimensional submanifold in such that its images under biholomorphisms , , are not equivalent to via any local volume-preserving holomorphic...
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 of CR Mappings.
Regularity of local embeddings of strictly pseudoconvex CR structures.
Résolution du pour les courants prolongeables définis dans un anneau
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.
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∞.
Some applications of Cauchy-Fantappie forms to (local) problems on
Some Totally Real Embeddings of Three-Manifolds.
Special normal form of a hyperbolic CR-manifold in ℂ⁴
We give a special normal form for a non-semiquadratic hyperbolic CR-manifold M of codimension 2 in ℂ⁴, i.e., a construction of coordinates where the equation of M satisfies certain conditions. The coordinates are determined up to a linear coordinate change.
Sur le prolongement holomorphe des fonctions C - R définies sur une hypersurfac réelle de classe C2 dans Cn.
Sur l'extension des fonctions C R
The Euler and Pontrjagin numbers of an n-manifold in ...n.