Related papers: Smooth embeddings with Stein surface images

Let D be a bounded strongly pseudoconvex domain in a Stein manifold S and let Y be a complex manifold. We prove that the graph of any continuous map from the closure of D to Y which is holomorphic in D admits a basis of open Stein…

This paper studies properly embedded surfaces in the 4-ball that are exotically knotted (i.e., topologically but not smoothly isotopic), and leverages this local phenomenon to study surfaces in larger 4-manifolds. The main results provide a…

With the aid of the technique of variation of domains developed in Memoirs of Amer. Math. Soc., Vol. 209, No. 984, 2011, we characterize the pseudoconvex domains with smooth boundary in Hopf surfaces which are not Stein.

Some generalizations and variations of the Fintushel-Stern rim surgery are known to produce smoothly knotted surfaces. We show that if the fundamental groups of their complements are cyclic, then these surfaces are topologically unknotted.…

We consider the topology for a class of hypersurfaces with highly nonisolated singularites which arise as exceptional orbit varieties of a special class of prehomogeneous vector spaces, which are representations of linear algebraic groups…

It is proved that any smooth manifold $\mathcal M$ of dimension $m$ admits a smooth polynomially convex embedding into $\mathbb C^n$ when $n\geq \lfloor 5m/4\rfloor$. Further, such embeddings are dense in the space of smooth maps from…

We construct examples of hyperbolic rational homology spheres and hyperbolic knot complements in rational homology spheres containing closed embedded totally geodesic surfaces.

A Heegaard diagram for a 3-manifold is regarded as a pair of simplexes in the complex of curves on a surface and a Heegaard splitting as a pair of subcomplexes generated by the equivalent diagrams. We relate geometric and combinatorial…

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…

Let E be a generic real submanifold of an almost complex manifold. The geometry of Bishop discs attached to E is studied in terms of the Levi form of E.

Motivated by classical theorems on minimal surface theory in compact hyperbolic three-manifolds, we investigate the questions of existence and deformations for least area minimal surfaces in complete noncompact hyperbolic three-manifold of…

A theorem of Mumford states that, on complex surfaces, any normal isolated singularity whose link is diffeomorphic to a sphere is actually a smooth point. While this property fails in higher dimensions, McLean asks whether the contact…

We consider the moduli space of bordered Riemann surfaces with boundary and marked points. Such spaces appear in open-closed string theory, particularly with respect to holomorphic curves with Lagrangian submanifolds. We consider a…

Turaev's shadow can be seen locally as the Stein factorization of a stable map. In this paper, we define the notion of stable map complexity for a compact orientable 3-manifold bounded by (possibly empty) tori counting, with some weights,…

We compute the signature of the Milnor fiber of certain type of non-isolated complex surface singularities, namely, images of finitely determined holomorphic germs. An explicit formula is given in algebraic terms. As a corollary we show…

We prove there exists a compact embedded minimal surface in a complete finite volume hyperbolic $3$-manifold $\mathcal{N}$. We also obtain a least area, incompressible, properly embedded, finite topology, $2$-sided surface. We prove a…

We characterize open embeddings of Stein spaces and of $C^\infty$-manifolds in terms of certain flatness-type conditions on the respective homomorphisms of function algebras.

We develop recursive formulas for the horizontal and vertical monodromies of a quasi-ordinary surface. These are monodromies associated to the Milnor fiber of a slice transverse to a component of the singular locus. In the course of working…

In this paper, we collect various structural results to determine when an integral homology $3$--sphere bounds an acyclic smooth $4$--manifold, and when this can be upgraded to a Stein manifold. In a different direction we study whether…

The paper is a survey of recent results in geometric representation theory describing group actions which induce multiplicity-free representations in the spaces of holomorphic functions. For connected compact Lie groups of automorphisms of…