Zhuo Liu

activity

20242026

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5 papers · 1 filter

math.CV2026

A Demailly-type approximation of singular Finsler metrics

Zhuo Liu

We establish a Demailly-type approximation theorem for singular Finsler metrics satisfying the multiple coarse $L^p$ extension property on holomorphic vector bundles. As an appli…

math.CV2025

An optimal $L^{2}$ extension for continuous $L^{2}$ -optimal Hermitian metrics

Zhuo Liu

In this paper, we obtain an optimal $L^{2}$ extension theorem for continuous $L^{2}$ -optimal Hermitian metric on bounded planer domains. As applications, we affirmatively answer a ques…

math.CV2025

Convolution Regularization Preserves the $L^{2}$ -Estimate Property for $(1, n)$ -Forms

Zhuo Liu

In this paper, we prove that the $L^2$-estimate property for $(1,n)$-forms is preserved under the standard convolution regularization. As applications, we show that any singula…

math.CV2024

Skoda's $L^{2}$ division theorem for $L^{2}$ -optimal pairs

Zhuo Liu, Xujun Zhang

We establish a Skoda-type $L^{2}$ division theorem for $L^{2}$ -optimal pairs, using a technique that combines a new Bochner-type inequality derived from the $L^{2}$ -optimal conditions an…

math.CV2024

A new characterization of $L^{2}$ -domains of holomorphy with null thin complements via $L^{2}$ -optimal conditions

Zhuo Liu, Xujun Zhang

In this paper, we show that the $L^{2}$ -optimal condition implies the $L^{2}$ -divisibility of $L^{2}$ -integrable holomorphic functions. As an application, we offer a new characterization…

A Demailly-type approximation of singular Finsler metrics

An optimal L2 extension for continuous L2-optimal Hermitian metrics

Convolution Regularization Preserves the L2-Estimate Property for (1,n)-Forms

Skoda's L2 division theorem for L2-optimal pairs

A new characterization of L2-domains of holomorphy with null thin complements via L2-optimal conditions

An optimal $L^{2}$ extension for continuous $L^{2}$ -optimal Hermitian metrics

Convolution Regularization Preserves the $L^{2}$ -Estimate Property for $(1, n)$ -Forms

Skoda's $L^{2}$ division theorem for $L^{2}$ -optimal pairs

A new characterization of $L^{2}$ -domains of holomorphy with null thin complements via $L^{2}$ -optimal conditions