• Bulletin of the Korean Mathematical Society
• /
• v.52 no.1
• /
• pp.85-103
• /
• 2015

We prove some sharp extremal distance results for functions in various spaces of analytic functions on bounded strictly pseudoconvex domains with smooth boundary. Also, we obtain atomic decompositions in multifunctional Bloch and weighted Bergman spaces of analytic functions on strictly pseudoconvex domains with smooth boundary, which extend known results in the classical case of a single function.

• Journal of the Korean Mathematical Society
• /
• v.54 no.6
• /
• pp.1787-1799
• /
• 2017

In this paper, we prove basic a priori estimate for the ${\bar{\partial}}$-Neumann problem on an annulus between two pseudoconvex submanifolds of a Stein manifold. As a corollary of the result, we obtain the global regularity for the ${\bar{\partial}}$-problem on the annulus. This is a manifold version of the previous results on pseudoconvex domains.

• East Asian mathematical journal
• /
• v.16 no.2
• /
• pp.391-399
• /
• 2000

• Journal of the Korean Mathematical Society
• /
• v.52 no.1
• /
• pp.113-124
• /
• 2015

We provide some relations between CR invariants of boundaries of strongly pseudoconvex domains and higher order asymptotic behavior of certain complete K$\ddot{a}$hler metrics of given domains. As a consequence, we prove a rigidity theorem of strongly pseudoconvex domains by asymptotic curvature behavior of metrics.

• Kyungpook Mathematical Journal
• /
• v.62 no.2
• /
• pp.323-331
• /
• 2022

In this paper, we present a formula for pseudohermitian curvatures on bounded strictly pseudoconvex domains in ℂ² with respect to the coefficients of adapted frames given by Graham and Lee in [3] and their structure equations. As an application, we will show that the pseudohermitian curvatures on strictly plurisubharmonic exhaustions of Thullen domains diverges when the points converge to a weakly pseudoconvex boundary point of the domain.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.2
• /
• pp.543-557
• /
• 2017

In this paper, we investigate the notion of q-pseudoconvexity to discuss and describe some geometric characterizations of q-pseudoconvex domains ${\Omega}{\subset}{\mathbb{C}}^n$. In particular, we establish that ${\Omega}$ is q-pseudoconvex, if and only if, for every boundary point, the Levi form of the boundary is semipositive on the intersection of the holomorphic tangent space to the boundary with any (n-q+1)-dimensional subspace $E{\subset}{\mathbb{C}}^n$. Furthermore, we prove that the Kiselman's minimum principal holds true for all q-pseudoconvex domains in ${\mathbb{C}}^p{\times}{\mathbb{C}}^n$ such that each slice is a convex tube in ${\mathbb{C}}^n$.

• Communications of the Korean Mathematical Society
• /
• v.11 no.1
• /
• pp.81-87
• /
• 1996

We will construct polynomials of degree 6 in z and $\bar{z}$ on $C^2$ which gives, via its coefficient $\beta$ as a parameter, a family of pseudoconvex domains $\Omega_\beta$ in $C^2$ with the origin being a boundary point, and show that the domains $\Omega_\beta$ has no peak functions of class $c^1$ at the origin and has no holomorphic support functions for $1 \leq \beta < \frac{9}{5}$.

• Journal of the Korean Mathematical Society
• /
• v.40 no.4
• /
• pp.727-745
• /
• 2003

We construct strongly pseudoconvex handlebodies in $C^{n}$ whose center is a quadratic strongly pseudoconvex domain with an attached flat Lagrangian disc or plane.

• Communications of the Korean Mathematical Society
• /
• v.27 no.4
• /
• pp.753-762
• /
• 2012

We prove some sharp extremal distance results for functions in weighted Bergman spaces on the upper halfplane. We also prove new analogous results in the context of bounded strictly pseudoconvex domains with smooth boundary.

• Journal of the Korean Mathematical Society
• /
• v.32 no.4
• /
• pp.661-678
• /
• 1995

In this paper we will estimate from above and below the values of the Bergman, Caratheodory and Kobayashi metrics for a vector X at z, where z is any point near a given point $z_0$ in the boundary of pseudoconvex domains in $C^n$.