Related papers: On a local characterization of pseudoconvex domain…

We give an explicit verifiable characterization of weakly pseudoconvex but locally nonconvexifiable hypersurfaces of finite type in dimension two. It is expressed in terms of a generalized model, which captures local geometry of the…

We prove a boundary version of the open mapping theorem for holomorphic maps between strongly pseudoconvex domains. That is, we prove that the local image of a holomorphic map $f:D\to D'$ close to a boundary regular contact point $p\in \de…

We study some special almost complex structures on strictly pseudoconvex domains. They appear naturally as limits under a nonisotroping scaling procedure and play a role of model objects in the geometry of almost complex manifolds with…

We use the method of pseudoanalytic continuation to obtain a characterization of spaces of holomorphic functions with boundary values in Besov spaces in terms of polynomial approximations.

The purpose of this paper is to provide some properties of maximal plurisubharmonic functions in a bounded domain of \mathbb{C}^n

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…

Our interest is the behavior of weak geodesics between two plurisubharmonic functions on pseudoconvex domains. We characterize the convergence condition along the geodesic between toric psh functions with a pole at origin on a unit ball in…

In recent work by Zimmer it was proved that if $\Omega\subset\mathbb C^n$ is a bounded convex domain with $C^\infty$-smooth boundary, then $\Omega$ is strictly pseudoconvex provided that the squeezing function approaches one as one…

This paper deals with some geometrical properties of solutions of some semilinear elliptic equations in bounded convex domains or convex rings. Constant boundary conditions are imposed on the single component of the boundary when the domain…

We establish a general uniqueness theorem for subharmonic functions of several variables on a domain. A corollary from this uniqueness theorem for holomorphic functions is formulated in terms of the zero subset of holomorphic functions and…

We give the parameter version of localization theorem for Bergman metric near the boundary points of strictly pseudoconvex domains. The approximation theorem for square integrable holomorphic functions on such domains in the spirit of…

We construct bounded pseudoconvex domains in $\mathbb{C}^2$ for which the Szeg\"o projection operators are unbounded on $L^p$ spaces of the boundary for all $p\not =2$.

In this paper, we introduce a concept of super-pseudoconvex domain. We prove that the solution of the Feffereman equation on a smoothly bounded strictly pseudoconvex domain $D$ in $\CC^n$ is plurisubharmonic if and only if $D$ is…

We show that every bounded domain $D$ in $\mathbb R^n$ with smooth $p$-convex boundary for $2\le p < n$ admits a smooth defining function $\rho$ which is $p$-plurisubharmonic on $\overline D$; if in addition $bD$ has no $p$-flat points then…

We prove that if $D\subset C^n$ is a bounded domain with real analytic boundary and D is pseudoconvex then the compact open topology in the group of holomorphic automorphisms of D is the topology of uniform convergence on D.

We give three proofs of the fact that a smoothly bounded, convex domain in R^n has smooth defining functions whose Hessians are non-negative definite in a neighborhood of the boundary of the domain.

We study the local and global versions of the convexity, which is closely related to the problem of extending a convex function on a non-convex domain to a convex function on the convex hull of the domain and beyond the convex hull. We also…

There exist several interesting results in the literature on subnormal operator tuples having their spectral properties tied to the geometry of strictly pseudoconvex domains or to that of bounded symmetric domains in $\C^n$. We introduce a…

A quantitative version of strong localization of the Kobayashi, Azukawa and Sibony metrics, as well as of the squeezing function, near a plurisubharmonic peak boundary point of a domain in $\Bbb C^n$ is given. As an application, the…

In the works of Darboux and Walsh it was remarked that a one to one self mapping of $\rr^3$ which sends convex sets to convex ones is affine. It can be remarked also that a $\calc^2$-diffeomorphism $F:U\to U^{'}$ between two domains in…