20 citations · 90 across the 21 of their papers we have counts for
21 papers
On highly degenerate CR maps of spheres
Giuseppe della Sala, Bernhard Lamel, Michael Reiter +1
For we classify the -degenerate smooth CR maps of the three-dimensional unit sphere into the -dimensional unit sphere. Each of these maps has image being…
The CR umbilical locus of a real ellipsoid in
Duong Ngoc Son
This paper concerns the CR umbilical locus of a real ellipsoid in , the set of points at which the ellipsoid can be osculated by a biholomorphic image of the sphere u…
An upper bound for the first positive eigenvalue of the Kohn Laplacian on Reinhardt real hypersurfaces
Gian Maria Dall'Ara, Duong Ngoc Son
A real hypersurface in is said to be Reinhardt if it is invariant under the standard -action on . Its CR geometry can be described in ter…
On CR maps from the sphere into the tube over the future light cone
Michael Reiter, Duong Ngoc Son
We determine all local smooth or formal CR maps from the unit sphere into the tube $\mathcal{T}:= \mathcal{C} \times i\mathbb{R}^3 \subset \mathb…
The holomorphic sectional curvature and "convex" real hypersurfaces in Kähler manifolds
Duong Ngoc Son
We prove a sharp lower bound for the Tanaka-Webster holomorphic sectional curvature of strictly pseudoconvex real hypersurfaces that are "semi-isometrically" immersed in a Kähler m…
The -Operator and Real Holomorphic Vector Fields
Friedrich Haslinger, Duong Ngoc Son
Let be a Hermitian manifold and a smooth weight function on . The -complex on weighted Bergman spaces of holomorphic -for…
The CR Ahlfors derivative and a new invariant for spherically equivalent CR maps
Bernhard Lamel, Duong Ngoc Son
We study a CR analogue of the Ahlfors derivative for conformal immersions of Stowe [23] that generalizes the CR Schwarzian derivative studied earlier by the second-named author [21…
On the Chern-Moser-Weyl tensor of real hypersurfaces
Michael Reiter, Duong Ngoc Son
We derive an explicit formula for the well-known Chern-Moser-Weyl tensor for nondegenerate real hypersurfaces in complex space in terms of their defining functions. The formula is…
Semi-isometric CR immersions of CR manifolds into Kähler manifolds and applications
Duong Ngoc Son
We study the second fundamental form of semi-isometric CR immersions from strictly pseudoconvex CR manifolds into Kähler manifolds. As an application, we give a precise condition f…
Eigenvalues of the Kohn Laplacian and deformations of pseudohermitian structures on CR manifolds
Amine Aribi, Duong Ngoc Son
We study the eigenvalues of the Kohn Laplacian on a closed embedded strictly pseudoconvex CR manifold as functionals on the set of positive oriented pseudohermitian structures $\ma…
CR-Analogue of Siu--formula and Applications to Rigidity problem for pseudo-Hermitian harmonic maps
Song-Ying Li, Duong Ngoc Son
We give several versions of Siu's -formula for maps from a strictly pseudoconvex pseudo-Hermitian manifold into a Kähler manifold …
The sharp upper bounds for the first positive eigenvalue of the Kohn-Laplacian on compact strictly pseudoconvex hypersurfaces
Song-Ying Li, Guijuan Lin, Duong Ngoc Son
We give sharp and explicit upper bounds for the first positive eigenvalue of the Kohn-Laplacian on compact strictly pseudoconvex hypersurfaces in i…
A family of compact strictly pseudoconvex hypersurfaces in without umbilical points
Peter Ebenfelt, Duong Ngoc Son, Dmitri Zaitsev
We prove the following: For , let be the bounded strictly pseudoconvex domain in given by \begin{equation*} (\log|z|)^2+(\log|w|)^2<ε^2. \end{equation*} Th…
The Schwarzian derivative and Möbius equation on strictly pseudo-convex CR manifolds
Duong Ngoc Son
The notion of Schwarzian derivative for locally univalent holomorphic functions on complex plane was generalized for conformal diffeomorphisms by Osgood and Stowe in 1992 [27]. We…
Umbilical points on three dimensional strictly pseudoconvex CR manifolds. I. Manifolds with -action
Peter Ebenfelt, Duong Ngoc Son
The question of existence of umbilical points, in the CR sense, on compact, three dimensional, strictly pseudoconvex CR manifolds was raised in the seminal paper by S.-S. Chern and…
A new characterization of the CR shpere and the sharp eigenvalue estimate for the Kohn Laplacian
Song-Ying Li, Duong Ngoc Son, Xiaodong Wang
Motivated by a sharp eigenvalue estimate for the Kohn Laplacian, we prove a theorem that characterizes the CR sphere in terms of the existence of a non-trivial complex-valued funct…
Holomorphic mappings between pseudoellipsoids in different dimensions
Peter Ebenfelt, Duong Ngoc Son
We give a necessary and sufficient condition for the existence of nondegenerate holomorphic mappings between pseudoellipsoidal real hypersurfaces, and provide an explicit parametri…
On the existence of holomorphic embeddings of strictly pseudoconvex algebraic hypersurfaces into spheres
Peter Ebenfelt, Duong Son
We show that there are strictly pseudoconvex, real algebraic hypersurfaces in $\bC^{n+1}$ that cannot be locally embedded into a sphere in $\bC^{N+1}$ for any . In fact, we show…
CR singular images of generic submanifolds under holomorphic maps
Jiri Lebl, André Minor, Ravi Shroff +2
The purpose of this paper is to organize some results on the local geometry of CR singular real-analytic manifolds that are images of CR manifolds via a CR map that is a diffeomorp…
Transversality of holomorphic mappings between real hypersurfaces in complex spaces of different dimensions
Peter Ebenfelt, Duong Ngoc Son
We consider holomorphic mappings between a smooth real hypersurface $M\subset \bC^{n+1}$ and another $M'\subset \bC^{N+1}$ with . We provide conditions guaranteeing th…
CR transversality of holomorphic mappings between generic submanifolds in complex spaces
Peter Ebenfelt, Duong Ngoc Son
We show that a holomorphic mapping sending one generic submanifold into another of the same dimension is CR transversal to the target submanifold provided that the source manifold…