arXiv subjects

Ngai-Fung Ng

Publications and source records attributed to Ngai-Fung Ng.

3 recordsLinked to original sources

arXiv2022

Limit of Weierstrass Measure on Stable Curves

The goal of the paper is to study the limiting behavior of the Weierstrass measures on a smooth curve of genus $g\geqslant 2$ as the curve approaches a certain nodal stable curve represented by a point in the Deligne-Mumford compactification $\bar{\mathcal M}_g$ of the moduli $\mathcal{M}_g$, including irreducible ones or those of compact type. As a consequence, the Weierstrass measures on a stable rational curve at the boundary of $\mathcal{M}_g$ are completely determined. In the process, the asymptotic behavior of the Bergman measure is also studied.

math.AG↗

arXiv2020

Complex Neumann Problem and Kohn's Algorithm

This article gives a rapid introduction to the complex Neumann problem and Kohn's algorithm for generating subelliptic estimate.

math.CV↗

arXiv2018

Properties of Caratheodory measure hyperbolic universal covers of compact Kahler manifolds

This article explores some properties of universal covers of compact Kahler manifolds, under the assumption of Caratheodory measure hyperbolicity. In particular, by comparing invariant volume forms, an inequality is established between the volume of canonical bundle of a compact Kahler manifolds and the Caratheodory measure of its universal cover (similar result as in [Kikuta 10]). Using similar method, an inequality is established between the restricted volume of canonical bundle of a compact Kahler manifolds and the restricted Caratheodory measure of its covering, solving a conjecture in [Kikuta 13].

math.DG↗