相关论文: Remarks on weakly pseudoconvex boundaries
In this paper we consider the following question: For bounded domains with smooth boundary, can strong pseudoconvexity be characterized in terms of the intrinsic complex geometry of the domain? Our approach to answering this question is…
Intersection homology with coefficients in a field restores Poincar\'e duality for some spaces with singularities, as pseudomanifolds. But, with coefficients in a ring, the behaviours of manifolds and pseudomanifolds are different. This…
We prove that all locally exposable points in a Stein compact in a complex space can be exposed along a given curve to a given real hypersurface. Moreover, the exposing map for a boundary point can be sufficiently close to the identity map…
We give an explicit construction of special strongly pseudoconvex domains in C^n of handlebody type, i.e., domains which are small tubes surrounding the union of a quadratic strongly pseudoconvex domain with an attached totally real handle.…
In this paper, we provide some characterizations of strong pseudoconvexity by the boundary behavior of intrinsic invariants for smoothly bounded pseudoconvex domains of finite type in $\mathbb{C}^2$. As a consequence, if such domain is…
We study the boundary regularity of proper holomorphic mappings between strictly pseudoconvex domains with $C^2$-boundaries.
We study proper holomorphic mappings between strictly pseudoconvex domains with low boundary regularity.
Let D be a smooth bounded pseudoconvex domain in C^n. We give several characterizations for the closure of D to have a strong Stein neighborhood basis in the sense that D has a defining function r such that {z\in C^n:r(z)<a} is pseudoconvex…
We show that a smooth bounded domain in $\mathbb{C}^n$ admitting partial pseudoconvex exhaustion remains partial pseudoconvex. The main ingredient of the proof is based on a new characterization of hyper-$q$-convex domains. Furthermore, we…
We study on the biholomorphic equivalence of a strongly pseudoconvex bounded domain with differentiable spherical boundary to an open ball, and we study on the biholomorphicity of a proper holomorphic self mapping of a strongly pseudoconvex…
We show how to construct a class of smooth bounded pseudoconvex domains whose boundary contains a given Stein manifold with strongly pseudoconvex boundary, having a prescribed codimension and D'Angelo class (a cohomological invariant…
We study the semicontinuity of automorphism groups for perturbations of domains in complex space or in complex manifolds. We provide a new approach to the study of such results for domains having minimal boundary smoothness. The emphasis in…
In this paper (a sequel to B. Drinovec Drnovsek and F. Forstneric, Holomorphic curves in complex spaces, Duke Math. J. 139 (2007), 203-253) we obtain existence and approximation results for closed complex subvarieties that are normalized by…
It is shown that two strictly pseudoconvex Stein domains with real analytic boundaries have biholomorphic universal coverings provided that their boundaries are locally biholomorphically equivalent. This statement can be regarded as a…
Using the concept of inner integral curves defined by Hirschowitz we generalize a recent result by Kim, Levenberg and Yamaguchi concerning the obstruction of a pseudoconvex domain spread over a complex homogeneous manifold to be Stein. This…
We prove that a relatively compact pseudoconvex domain with smooth boundary in an almost complex manifold admits a bounded strictly plurisubharmonic exhaustion function. We use this result for the study of convexity and hyperbolicity…
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.
Pseudoconvexity of a domain in $\Bbb C^n$ is described in terms of the existence of a locally defined plurisubharmonic/holomorphic function near any boundary point that is unbounded at the point.
We study the stable embedding problem for a CR family of 3-dimensional strongly pseudoconvex CR manifolds with each fiber bounding a stein manifold.
We consider the behavior of the nonlocal minimal surfaces in the vicinity of the boundary. By a series of detailed examples, we show that nonlocal minimal surfaces may stick at the boundary of the domain, even when the domain is smooth and…