Related papers: Local normal forms of singular Levi-flat hypersurf…

We prove the existence of normal forms for some local real-analytic Levi-flat hypersurfaces with an isolated line singularity. We also give sufficient conditions for that a Levi-flat hypersurface with a complex line as singularity to be a…

We prove the existence of a normal form for a real-analytic Levi-flat hypersurface defined by the vanishing of the real part of a holomorphic function with a Morse-Bott singularity. As a consequence, we recover the Burns-Gong normal form…

Let $F(z)=\mathcal{R}e(P(z)) + h.o.t$ be such that $M=(F=0)$ defines a germ of real analytic Levi-flat at $0\in\mathbb{C}^{n}$, $n\geq{2}$, where $P(z)$ is a homogeneous polynomial of degree $k$ with an isolated singularity at…

In this paper, we study the real hypersurfaces $M$ in $\mathbb C^2$ at points $p\in M$ of infinite type. The degeneracy of $M$ at $p$ is assumed to be the least possible, namely such that the Levi form vanishes to first order in the CR…

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.

We construct normal forms for Levi degenerate hypersurfaces of finite type in $\mathbb C^2$. As one consequence, an explicit solution to the problem of local biholomorphic equivalence is obtained. Another consequence determines the…

We study the singular set of a singular Levi-flat real-analytic hypersurface. We prove that the singular set of such a hypersurface is Levi-flat in the appropriate sense. We also show that if the singular set is small enough, then the…

We consider hypersurfaces of finite type in a direct product space ${\mathbb R}^2 \times {\mathbb R}^2$, which are analogues to real hypersurfaces of finite type in ${\mathbb C}^2$. We shall consider separately the cases where such…

The purpose of this article is to classify the real hypersurfaces in complex space forms of dimension 2 that are both Levi-flat and minimal. The main results are as follows: When the curvature of the complex space form is nonzero, there is…

We consider the problem of describing the local biholomorphic equivalence class of a real-analytic hypersurface $M$ at a distinguished point $p_0\in M$ by giving a normal form for such objects. In order for the normal form to carry useful…

We explicitly describe germs of strongly pseudoconvex non-spherical real-analytic hypersurfaces $M$ at the origin in $\CC^{n+1}$ for which the group of local CR-automorphisms preserving the origin has dimension $d_0(M)$ equal to either…

We present a proof of the existence and uniqueness theorem of a normalizing biholomorphic mapping to Chern-Moser normal form. The explicit form of the equation of a chain on a real hyperquadric is obtained. We show a family of normal forms…

We study holomorphic foliations tangent to singular real-analytic Levi-flat hypersurfaces in compact complex manifolds of complex dimension two. We give some hypotheses to guarantee the existence of dicritical singularities of these…

In this paper we construct a large class of new normal forms for Levi-nondegenerate real hypersurfaces in complex spaces. We adopt a general approach illustrating why these normal forms are natural and which role is played by the celebrated…

The regular type of a real hyper-surface M in an (almost) complex manifold at some point p is the maximal contact order at p of M with germs of non singular (pseudo) holomorphic disks. The main purpose of this paper is to give two intrinsic…

Real-analytic Levi-flat codimension two CR singular submanifolds are a natural generalization to ${\mathbb{C}}^m$, $m > 2$, of Bishop surfaces in ${\mathbb{C}}^2$. Such submanifolds for example arise as zero sets of mixed-holomorphic…

We study singular real analytic Levi-flat subsets invariant by singular holomorphic foliations in complex projective spaces. We give sufficient conditions for a real analytic Levi-flat subset to be the pull-back of a semianalytic Levi-flat…

We study singular real-analytic Levi-flat hypersurfaces in complex projective space. We define the rank of an algebraic Levi-flat hypersurface and study the connections between rank, degree, and the type and size of the singularity. In…

Let $H \subset {\mathbb P}^n$ be a real-analytic subvariety of codimension one induced by a real-analytic curve in the Grassmannian $G(n+1,n)$. Assuming $H$ has a global defining function, we prove $H$ is Levi-flat, the closure of its…

We provide normal forms for singularities of analytic hypersurfaces in $({\mathbb C}^n,0)$, using holomorphic vector fields.