Related papers: Th\'eor\`eme de Hartogs-Bochner dans $P_2(\mathbb{…

We prove the following Hartogs-Bochner type theorem: Let $M$ be a connected $C^2$ hypersurface of $P_n(\mathbb{C})$ ($n\geq 2$) which divides $P_n(\mathbb{C})$ in two connected open sets $\Omega_1$ and $\Omega_2$. Then there exists $i \in…

Let M be a compact, connected, C^2-smooth and globally minimal hypersurface M in P_2(C) which divides the projective space into two connected parts U^{+} and U^{-}. We prove that there exists a side, U^- or U^+, such that every continuous…

We prove an analog of the classical Hartogs extension theorem for CR $L^{2}$ functions defined on boundaries of certain (possibly unbounded) domains on coverings of strongly pseudoconvex manifolds. Our result is related to a problem posed…

Let $\Omega\subset\mathbb{C}^n$, $n\geq 2$, be a domain with smooth connected boundary. If $\Omega$ is relatively compact, the Hartogs-Bochner theorem ensures that every CR distribution on $\partial\Omega$ has a holomorphic extension to…

We develop a classification theory for real-analytic hypersurfaces in $\mathbb C^2$ in the case when the hypersurface is of {\em infinite type} at the reference point. This is the remaining, not yet understood case in $\mathbb C^2$ in the…

Let $M \subset {\mathbb{C}}^{n+1}$, $n \geq 2$, be a real codimension two CR singular real-analytic submanifold that is nondegenerate and holomorphically flat. We prove that every real-analytic function on $M$ that is CR outside the CR…

A generalization of the Hartogs theorem is proved for a class of Tubes structures. We assume that the intervening commutative Lie algebra admits at least a number of globally solvable generators greater or equal to the structure…

If a mapping of several complex variables into projective space is holomorphic in each pair of variables, then it is globally holomorphic.

This paper is devoted to various applications of Hardy-Sobolev type inequalities. We derive a new $L^2$ estimate for the $\bar{\partial}-$equation on ${\mathbb C}^n$ which yields a quantitative generalization of the Hartogs extension…

The purpose of this article is twofold. The first is to prove a second main theorem for meromorphic mappings of $\C^m$ into a complex projective variety intersecting hypersurfaces in subgeneral position with truncated counting functions.…

We establish Marstrand-type projection theorems for orthogonal projections along geodesics onto m-dimensional subspaces of hyperbolic $n$-space by a geometric argument. Moreover, we obtain a Besicovitch-Federer type characterization of…

Let X be a connected normal complex space of dimension n>=2 which is (n-1)-complete, and let p: M -> X be a resolution of singularities. By use of Takegoshi's generalization of the Grauert-Riemenschneider vanishing theorem, we deduce…

Homological Projective duality (HP-duality) theory, introduced by Kuznetsov [42], is one of the most powerful frameworks in the homological study of algebraic geometry. The main result (HP-duality theorem) of the theory gives complete…

First, we classify proper biharmonic Hopf real hypersurfaces in $\mathbb{C}P^2$. Next, we classify proper biharmonic real hypersurfaces with two distinct principal curvatures in $\mathbb{C}P^n$, where $n\geq 2$. Finally, we prove that…

We establish Marstrand-type as well as Besicovich-Federer-type projection theorems for closest-point projections onto hyperplanes in the normed space $\mathbb{R}^{n}$. In particular, we prove that if a norm on $\mathbb{R}^{n}$ is…

Every small category $C$ has a classifying space $BC$ associated in a natural way. This construction can be extended to other contexts and set up a fruitful interaction between categorical structures and homotopy types. In this paper we…

In this paper, we aim to establish a new shape theory, compact Hausdorff shape (CH-shape) for general Hausdorff spaces. We use the "internal" method and direct system approach on the homotopy category of compact Hausdorff spaces. Such a…

We prove that two closed subsets of complex space $\C^n$ with corresponding complex homothetic sections (projections) are complex homothetic. The proof uses a new Helly-type theorem for cosets of closed subgroups of $\S ^1$.

We establish extension theorems for separately holomorphic mappings defined on sets of the form W\setminus M with values in a complex analytic space which possesses the Hartogs extension property. Here W is a 2-fold cross of arbitrary…

In this note, we prove that the holonomy map from the set of equivalence classes of projective structures of parabolic type on non compact surfaces to the set of equivalence classes of parabolic representations of the fundamental group of…