arXiv subjects

Kang-Hyurk Lee

Publications and source records attributed to Kang-Hyurk Lee.

9 recordsLinked to original sources

arXiv2026

Kähler Hyperbolicity Modulus for Simply-connected Kähler Hyperbolic manifolds

This paper investigates the Kähler hyperbolicity modulus on complete Kähler manifolds, with a particular focus on hyperconvex domains and bounded strongly pseudoconvex domains. Our main result establishes a lower bound for the Kähler hyperbolicity modulus in terms of the boundary behavior of the gradient length of a plurisubharmonic function. As applications, we compute the Kähler hyperbolicity modulus for bounded symmetric domains. Furthermore, we obtain lower bounds for the Kähler hyperbolicity modulus on bounded strongly pseudoconvex domains equipped with Kähler-Einstein metrics or Bergman metrics.

math.CV↗

arXiv2026

A Sharp Lower Bound for the Spectrum of the Hodge Laplacian on Kähler Hyperbolic Manifolds and its Applications

In this paper, we establish a sharp lower bound for the spectrum of the Hodge Laplacian on Kähler hyperbolic manifolds. This bound is expressed explicitly in terms of the supremum norm of the 1-form associated with the Kähler hyperbolic structure. As an application, we obtain explicit spectral lower bounds for bounded symmetric domains.

math.DG↗

arXiv2025

On the Kähler-hyperbolicity of bounded symmetric domains

In this paper, we characterize the Kähler-hyperbolicity length of a bounded symmetric domain, defined by its rank and genus, as a unique constant determined by a constant gradient length of a special Bergman potential. Additionally, we establish a characterization of the lower bound of $L^\infty$ norm of the gradient length of any Bergman potential.

math.CV↗

arXiv2022

A characterization of the unit ball by a Kähler-Einstein potential

We will show that a universal covering of a compact Kähler manifold with ample canonical bundle is the unit ball if it admits a global potential function of the Kähler-Einstein metric whose gradient length is a minimal constant. As an application, we will extend the Wong-Rosay theorem to a complex manifold without boundary.

math.CV↗

arXiv2022

Almost CR manifolds with contracting CR automorphism

In this paper, we deal with a strongly pseudoconvex almost CR manifold with a CR contraction. We will prove that the stable manifold of the CR contaction is CR equivalent to the Heisenberg group model.

math.CV↗

arXiv2020

Existence of a complete holomorphic vector field via the Kähler-Einstein metric

In this paper, we study the existence of a complete holomorphic vector fields on a strongly pseudoconvex complex manifold admitting a negatively curved complete Kähler-Einstein metric and a discrete sequence of automorphisms. Using the method of potential scaling, we will show that there is a potential function of the Kähler-Einstein metric whose differential has a constant length. Then we will construct a complete holomorphic vector field from the gradient vector field of the potential function.

math.CV↗

arXiv2020

A method of potential scaling in the study of pseudoconvex domains with noncompact automorphism group

The affine scaling method has been a typical approach to study complex domains with noncompact automorphism group. In this article, we will introduce an alternative approach, so called, the method of potential scaling to construct a certain class of potential functions of the Kähler-Einstein metric. We will also prove that if a bounded pseudoconvex domain admits a potential function of the Kähler-Einstein metric whose differential has constant length, then there is an $1$-parameter family of automorphisms.

math.CV↗

arXiv2020

A certain Kähler potential of the Poincaré metric and its characterization

We will show a rigidity of a Kähler potential of the Poincaré metric with a constant length differential.

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↗