Related papers: Meromorphic convexity on Stein manifolds

This paper examines the broad structure on Stein manifolds and how it generalizes the notion of a domain of holomorphy in $\mathbb C^n$. Along with this generalization, we see that Stein manifolds share key properties from domains of…

The notion of meromorphic convexity is defined and studied on complex manifolds. Using this notion, in analogy with Stein manifolds, a new class of complex manifolds, called {\calligra M }-manifolds, is introduced. This is a class of…

We prove that a Stein manifold of dimension $d$ admits a proper holomorphic embedding into any Stein manifold of dimension at least $2d+1$ satisfying the holomorphic density property. This generalizes classical theorems of Remmert, Bishop…

We generalize a criterion for the density property of Stein manifolds. As an application, we give a new, simple proof of the fact that the Danielewski surfaces have the algebraic density property. Furthermore, we have found new examples of…

We study stable rationality properties of conic bundles over rational surfaces.

We introduce the notion of a generalized complex (GC) Stein manifold and provide complete characterizations in three fundamental aspects. First, we extend Cartan's Theorem A and B within the framework of GC geometry. Next, we define…

In this paper we prove Cartan theorems A and B for Stein manifolds over certain discrete valuation rings.

We present a classification of 2-dimensional, taut, Stein manifolds with a proper $\R$-action. For such manifolds the globalization with respect to the induced local $\C$-action turns out to be Stein. As an application we determine all…

We prove an analog of the classical Hartogs extension theorem for certain (possibly unbounded) domains on coverings of Stein manifolds.

We study the spaces of rational curves on Fano threefolds with Gorenstein terminal singularities. We generalize the results regarding Geometric Manin's Conjecture for smooth Fano threefolds, including the classification of subvarieties with…

In this paper we survey results on the existence of holomorphic embeddings and immersions of Stein manifolds into complex manifolds. Most results pertain to proper maps into Stein manifolds. We include a new result saying that every…

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

We give some rationality constructions for Fano threefolds with canonical Gorenstein singularities.

It is proved that the local smoothing conjecture for wave equations implies certain improvements on Stein's analytic family of maximal spherical means. Some related problems are also discussed.

We describe a convex relaxation for the Gilbert-Steiner problem both in $R^d$ and on manifolds, extending the framework proposed in [9], and we discuss its sharpness by means of calibration type arguments. The minimization of the resulting…

We generalize symplectic convexity theorems for Hamiltonian actions with proper momentum maps to symplectic actions on orbifolds with mod-$\Gamma$ proper momentum maps.

A Stein covering of a complex manifold may be used to realise its analytic cohomology in accordance with the Cech theory. If, however, the Stein covering is parameterised by a smooth manifold rather than just a discrete set, then we…

The usual notion of set-convexity, valid in the classical Euclidean context, metamorphoses into several distinct convexity types in the more general Riemannian setting. By studying this phenomenon in reverse, we characterize complete…

We discuss various known generalizations of the classical Hartogs' extension theorem on Stein spaces with arbitrary singularities and present an analytic proof based on d-bar methods.

In this note, we present the concavity of the minimal $L^2$ integrals related to multiplier ideals sheaves on Stein manifolds. As applications, we obtain a necessary condition for the concavity degenerating to linearity, a characterization…