arXiv subjects

Kang-Tae Kim

Publications and source records attributed to Kang-Tae Kim.

At least 19 recordsLinked to original sources

arXiv2025

A Selection Theorem for the Carathéodory Kernel Convergence of Pointed Domains

We present a selection theorem for domains in $\mathbb{C}^n$, $n\ge 1$, which states that any tamed sequence of pointed connected open subsets admits a subsequence convergent to its own kernel in the sense of Carathéodory. Not only is this analogous to the well-known Blaschke selection theorem for compact convex sets, but it fits better in the study of normal families of holomorphic maps with varying domains and ranges.

math.CV↗

arXiv2022

Topological invariants and Holomorphic Mappings

Invariants for Riemann surfaces covered by the disc and for hyperbolic manifolds in general involving minimizing the measure of the image over the homotopy and homology classes of closed curves and maps of the $k$-sphere into the manifold are investigated. The invariants are monotonic under holomorphic mappings and strictly monotonic under certain circumstances. Applications to holomorphic maps of annular regions in $\mathbb{C}$ and tubular neighborhoods of compact totally real submanifolds in general in $\mathbb{C}^n$, $n \geq 2$, are given. The contractibility of a hyperbolic domain with contracting holomorphic mapping is explained.

math.CV↗

arXiv2020

Infinite dimensional holomorphic homogeneous regular domains

We extend the concept of a finite dimensional {\it holomorphic homogeneous regular} (HHR) domain and some of its properties to the infinite dimensional setting. In particular, we show that infinite dimensional HHR domains are domains of holomorphy and determine completely the class of infinite dimensional bounded symmetric domains which are HHR. We compute the greatest lower bound of the squeezing function of all HHR bounded symmetric domains, including the two exceptional domains. We also show that uniformly elliptic domains in Hilbert spaces are HHR.

math.CV↗

arXiv2020

Functions holomorphic along a $C^1$ pencil of holomorphic discs

The main purpose of this article is to present a generalization of Forelli's theorem for the functions holomorphic along a general pencil of holomorphic discs. This generalizes the main result of \cite{JKS13} and the original Forelli's theorem, and furthermore, answers one of the problems posed in \cite{Chirka06}.

math.CV↗

arXiv2017

The $\overline{\partial}$-equation on variable strictly pseudoconvex domains

We investigate regularity properties of the $\overline{\partial}$-equation on domains in a complex euclidean space that depend on a parameter. Both the interior regularity and the regularity in the parameter are obtained for a continuous family of pseudoconvex domains. The boundary regularity and the regularity in the parameter are also obtained for smoothly bounded strongly pseudoconvex domains.

math.CV↗

arXiv2017

Homogeneous almost complex manifolds and their compact quotients

The paper investigates the (non)existence of compact quotients, by a discrete subgroup, of the homogeneous almost-complex strongly-pseudoconvex manifolds disconvered and classified by Gaussier-Sukhov and K.-H. Lee.

math.CV↗

arXiv2016

The Riemann mapping theorem from Riemann's viewpoint

This article presents a clear proof of the Riemann Mapping Theorem via Riemann's method, uncompromised by any appeals to topological intuition.

math.CV↗

arXiv2016

On boundary points at which the squeezing function tends to one

J. E. Fornaess has posed the question whether the boundary point of smoothly bounded pseudoconvex domain is strictly pseudoconvex, if the asymptotic limit of the squeezing function is 1. The purpose of this paper is to give an affirmative answer when the domain is in C^2 with smooth boundary of finite type in the sense of D'Angelo.

math.CV↗

arXiv2014

Positivity and completeness of invariant metrics

We present a method for constructing global holomorphic peak functions from local holomorphic support functions for broad classes of unbounded domains. As an application, we establish a method for showing the positivity and completeness of invariant metrics including the Bergman metric mainly for the unbounded domains.

math.CV↗

arXiv2014

Bergman and Caratheodory metrics of the Kohn-Nirenberg domains

The Kohn-Nireberg domains are unbounded domains in the complex Euclidean space of dimension 2 upon which many outstanding questions are yet to be explored. The primary aim of this article is to demonstrate that the Bergman and Caratheodory metrics of any Kohn-Nirenberg domains are positive and complete.

math.CV↗

arXiv2014

On the generalization of Forelli's theorem

The purpose of this paper is to present a solution to perhaps the final remaining case in the line of study concerning the generalization of Forelli's theorem on the complex analyticity of the functions that are: (1) $\mathcal{C}^\infty$ smooth at a point, and (2) holomorphic along the complex integral curves generated by a contracting holomorphic vector field with an isolated zero at the same point.

math.CV↗

arXiv2013

Stably-interior points and the Semicontinuity of the Automorphism group

The first result is the semicontinuity of automorphism groups for the collection of complex two-dimensional bounded pseudoconvex domains with smooth boundary of finite D'Angelo type. The method of proof is new so that it simplifies the previous proof of earlier semicontinuity theorems on bounded strongly pseudoconvex daomains by Greene and Krantz in the early 1980s.

math.CV↗

arXiv2013

On the uniform squeezing property and the squeezing function

We describe the boundary behaviors of the squeezing functions for all bounded convex domains in $\mathbb{C}^n$ and bounded domains with a $C^2$ strongly convex boundary point.

math.CV↗

arXiv2012

On the tangential holomorphic vector fields vanishing at an infinite type point

Let (M,p) be a smooth non-Leviflat CR hypersurface germ in complex Euclidean space of dimension 2 where p is of infinite type. The purpose of this article is to investigate the holomorphic vector fields tangent to (M,p) vanishing at p.

math.CV↗

arXiv2011

A generalization of Forelli's theorem

The purpose of this paper is to present a generalization of Forelli's theorem. In particular, we prove an all dimensional version of the two-dimensional theorem of Chirka of 2005.

math.CV↗

arXiv2011

Semi-continuity of Automorphism Groups of Strongly Pseudoconvex Domains: the low differentiability case

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 this study is on the low differentiability assumption and the new methodology developed accordingly.

math.CV↗

arXiv2008

Functions holomorphic along holomorphic vector fields

The main result of the paper is the following generalization of Forelli's theorem: Suppose F is a holomorphic vector field with singular point at p, such that F is linearizable at p and the matrix is diagonalizable with the eigenvalues whose ratios are positive reals. Then any function $ϕ$ that has an asymptotic Taylor expansion at p and is holomorphic along the complex integral curves of F is holomorphic in a neighborhood of p. We also present an example to show that the requirement for ratios of the eigenvalues to be positive reals is necessary.

math.CV↗

arXiv2008

CR manifolds admitting a CR contraction

We classify the germs of $\mathcal{C}^\infty$ CR manifolds that admit a smooth CR contraction. We show that such a CR manifold is embedded into $\CC^n$ as a real hypersurface defined by a polynomial defining function consisting of monomials whose degrees are completely determined by the extended resonances of the contraction. Furthermore the contraction map extends to a holomorphic contraction that coincides in fact with its polynomial normal form. Consequently, several results concerning Complex and CR geometry are derived.

math.CV↗