相关论文: The topology of rationally and polynomially convex…

This work provides two sufficient conditions in terms of sections or projections for a convex body to be a polytope. These conditions are necessary as well.

We will use different way (in this work) from the existing methods in the literature which speaking in the separation of convex sets was carried out by hyperplanes. We are examining the behavior of convex set which is the domain of convex…

In the paper the complex geodesics of a convex domain in $\mathbb C^n$ are studied. One of the main results of the paper provides certain necessary condition for a holomorphic map to be a complex geodesic for a convex domain in $\mathbb…

We survey some results on real rational surfaces focused on their topology and their birational geometry.

We establish some upper and lower bounds of the rational topological complexity for certain classes of elliptic spaces. Our techniques permit us in particular to show that the rational topological complexity coincides with the dimension of…

Rationally convex topological embeddings of compact surfaces (closed or with boundary) into $\mathbb{C}^2$ are constructed.

We study proper holomorphic mappings between strictly pseudoconvex domains with low boundary regularity.

The paper is concerned with the boundary behaviour of polynomially and rationally convex hulls in pseudoconvex domains in $\mathbb{C}^n$. As an application, it is shown that every connected polynomially or rationally convex compact set with…

In this paper, we first establish several general sufficient conditions for the biholomorphic convex mappings on the bounded convex balanced domain $D_{p}^n(p_{j}\geq 2,j=1,\cdots,n)$ in $C^{n}$, which extend some related results of earlier…

Under a mild technical assumption, we prove a necessary and sufficient condition for a totally real compacdt set in $\mathbb{C}^n$ to be rationally convex. This generalizes a classical result of Duval-Sibony

We introduce different notions of polynomial convexity with bounds on degrees of polynomials in $\mathbb C^n$. We provide some examples in higher dimensions and show necessary and sufficient conditions for polynomial convexity with degree…

The aim of this paper is to provide a complete and simple characterization of functions with domain in a topological real vector space whose epigraph is strictly convex.

A sufficient condition for $\bar{\partial}$ to have closed range is given for pseudoconvex, possibly unbounded domains in $\mathbb{C}^n$.

In this paper we present algorithms for computing the topology of planar and space rational curves defined by a parametrization. The algorithms given here work directly with the parametrization of the curve, and do not require to compute or…

In this paper we analyze the problem of the geodesic connectedness of subsets of Riemannian manifolds. By using variational methods, the geodesic connectedness of open domains (whose boundaries can be not differentiable and not convex) of a…

We address the problem of topology of quadrature domains, namely we give upper bounds on the connectivity of the domain in terms of the number of nodes and their multiplicities in the quadrature identity.

In Part I we gave a polynomial growth lower-bound for the number of nodal domains of a Hecke-Maass cuspform in a compact part of the modular surface, assuming a Lindel\"of hypothesis. That was a consequence of a topological argument and…

We investigate regularity properties of the $\overline{\partial}$-equation on domains in a complex euclidean space that depend on a parameter. Both the interior regularity and the regularity in the parameter are obtained for a continuous…

We give description of rational solutions of polynomial-equations.

In the paper we show the existence of different types of peak functions in classes of $\mathbb C$-convex domains. As one of tools used in this context is a result on preserving the regularity of $\mathbb C$-convex domains under projection.