arXiv subjects

Ye-Won Luke Cho

Publications and source records attributed to Ye-Won Luke Cho.

7 recordsLinked to original sources

arXiv2026

Bottom of the spectrum of complete noncompact Kähler manifolds

We present a survey on the bottom of the spectrum of the Hodge Laplacian on complete noncompact Kähler manifolds, with particular emphasis on Kähler hyperbolic manifolds and bounded symmetric domains. We also discuss theorems regarding the upper bounds for the bottom of the spectrum under Ricci and bisectional curvature assumptions, along with rigidity results for manifolds attaining the maximal bottom of the spectrum. Throughout the article, we propose several open problems.

math.DG↗

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

Continuity of solutions to complex Monge-Ampère equations on compact Kähler spaces

We prove the continuity of bounded solutions to complex Monge-Ampère equations on reduced, locally irreducible compact Kähler spaces. This in particular implies that any singular Kähler-Einstein potentials constructed in \cite{EGZ09} and \cite{Tsuji88, TianZhang06, ST17} are continuous. We also provide an affirmative answer to a conjecture in \cite{EGZ09} by showing that a resolution of any compact normal Kähler space satisfies the continuous approximation property. Finally, we settle the continuity of the potentials of the weak Kähler-Ricci flows \cite{ST17, GLZ20} on compact Kähler varieties with log terminal singularities.

math.DG↗

arXiv2023

A survey on generalizations of Forelli's theorem and related pluripotential methods

We present a survey on recent developments of generalizations of Forelli's analyticity theorem and related pluripotential methods.

math.CV↗

arXiv2023

A new plurisubharmonic capacity and functions holomorphic along holomorphic vector fields

The main purpose of this article is to present a generalization of Forelli's theorem for functions holomorphic along a suspension of integral curves of a diagonalizable vector field of aligned type. For this purpose, we develop a new capacity theory that generalizes the theory of projective capacity introduced by Siciak \cite{Siciak82}. Our main theorem improves the results of \cite{KPS09}, \cite{Cho22} as well as the original Forelli's theorem.

math.CV↗

arXiv2022

Localization of Forelli's theorem

The main purpose of this article is to present a localization of Forelli's theorem for the functions holomorphic along a standard suspension of linear discs. This generalizes one of the main results of \cite{CK21} and the original Forelli's theorem.

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↗