On Huang-Yin's Normal Form I
It is formally constructed a normal form for a class of real-formal surfaces defined near a CR Singularity.
math.CV↗
arXiv subjects
Valentin Burcea
Publications and source records attributed to Valentin Burcea.
Special Classes of CR Singularities II
It is constructed a Formal Normal Form for a Special Class of Real-Smooth Submanfolds in $\mathbb{C}^{2N}$.
math.CV↗
Special Classes of CR Singularities I
It is proven an analogue of The Theorem of Moser according to an iterative normalization procedure depending on Generalized Fischer Decompositions.
math.CV↗
Real-Smooth Hypersurfaces in $\mathbb{C}^{N+1}$
It is constructed a formal normal form, using an iterative normalization procedure, for a large class of Real-Smooth Hypersurfaces in Complex Spaces.
math.CV↗
CR Singularities and Generalizations of Moser's Theorem II
Let a real-analytic manifold $M$ formally (holomorphically) equivalent to the following model \begin{equation*}w=z_{1}\overline{z}_{1}+\dots+z_{N}\overline{z}_{N}+\lambda_{1}\left(z_{1}^{2}+\overline{z}_{1}^{2}\right)+\dots+\lambda_{N}\left(z_{N}^{2}+\overline{z}_{N}^{2}\right),{equation*} assuming that $$ \lambda_{1},\dots, \lambda_{N}\in \left[0,\frac{1}{2}\right).$$ It is proven that $M$ is holomorphically equivalent to this model by developing a partial normal form for such real-analytic submanifold using generalized Fischer Decompositions. In particular, there are defined certain Spaces of Normalizations used also in proving other analogues of The Theorem of Moser in certain non-equidimensional situations. There presented also other applications for the methods considered.
math.CV↗
Formal Equivalences in $\mathbb{C}^{4}$
There are solved standard problems related to Formal (Holomorphic) Segre preserving Mappings of non-trivial Real-Formal Hypersurfaces in $\mathbb{C}^{2}$.
math.CV↗
Formal Embeddings between $\mathcal{BSD}$-Models
It is studied the Classification Problem for Formal (Holomorphic) Embeddings between (open pieces of) Shilov Boundaries of Bounded Symmetric Domains of First Type.
math.CV↗
CR Singularities and Generalizations of Moser's Theorem I
There are proven few analogues of the Theorem of Moser using The Approximation Theorem of Artin.
math.CV↗
Real Submanifolds in Complex Spaces: Upgrades
It is proven a new analogue of the Theorem of Moser in a generalized context defined by Shilov Boundaries of Bounded and Symmetric Domains.
math.CV↗
Normal Forms and Degenerate CR Singularities
It is constructed a normal form for a class of real-smooth surfaces M\subset\mathbb{C}^{2} defined near a degenerate CR singularity.
math.CV↗
On a family of analytic discs attached to a real submanifold $M\subset\mathbb{C}^{N+1}$
We construct a family of analytic discs attached to a real submanifold M \subset $\mathbb{C}^{N+1}$ of codimension $2$ defined near a CR singularity.
math.CV↗
A normal form for a real 2-codimensional submanifold in $\mathbb{C}^{N+1}$ near a CR singularity
We construct a formal normal form for a real 2-codimensional submanifold $M\subset\mathbb{C}^{N+1}$ near a CR singularity approximating the sphere. This result gives a higher dimensional extension of Huang-Yin's normal form in $\mathbb{C}^{2}$.
math.CV↗