Zhiwei Wang

activity

20132026

most citedNew characterizations of plurisubharmonic functions and positivity of direct image sheaves

20 citations · 41 across the 22 of their papers we have counts for

collaborators

23 papers

math.CV2026

On the extension of Kähler currents on compact complex manifolds

Jiafu Ning, Kai Pang, Haoyuan Sun +2

Let $(X, ω)$ be a compact Kähler manifold and let $V \subset X$ be a closed complex submanifold. Coman-Guedj-Zeriahi proposed the problem: is every $ω ∣_{V}$ -plurisubharmonic function o…

math.CV2026

Capacity Stability of Complex Monge-Ampère Equations with Moving Prescribed Singularities

Kai Pang, Haoyuan Sun, Zhiwei Wang +1

For complex Monge-Ampère equations with moving big cohomology classes and prescribed model singularities of positive Monge-Ampère mass, we prove that, under total variation converg…

math.CV2025

Macaulay representation of the prolongation matrix and the SOS conjecture

Zhiwei Wang, Chenlong Yue, Xiangyu Zhou

Let $z \in C^{n}$ , and let $A (z, z ˉ)$ be a real valued diagonal bihomogeneous Hermitian polynomial such that $A (z, z ˉ) ∥ z ∥^{2}$ is a sum of squares, where $∥ z ∥$ den…

math.CV2025

Log truncated threshold and zero mass conjecture

Fusheng Deng, Yinji Li, Qunhuan Liu +2

For plurisubharmonic functions $φ$ and $ψ$ lying in the Cegrell class of $B^{n}$ and $B^{m}$ respectively such that the Lelong number of $φ$ at the origin vanishes, w…

math.CV2024

On the Range of a class of Complex Monge-Ampère operators on compact Hermitian manifolds

Yinji Li, Zhiwei Wang, Xiangyu Zhou

Let $(X, ω)$ be a compact Hermitian manifold of complex dimension $n$ . Let $β$ be a smooth real closed $(1, 1)$ form such that there exists a function $ρ\in \mbox{PSH}(X,β)\cap L^{\i…

math.CV2023

A note on Demailly's transcendental Morse inequalities conjecture

Yinji Li, Zhiwei Wang, Xiangyu Zhou

Let $(X, ω)$ be an $n$ -dimensional compact Hermitian manifold with $ω$ a pluriclosed Hermitian metric, i.e. $d d^{c} ω = 0$ . Let ${α}, {β} \in H_{B C}^{1, 1} (X, R)$ be two nef clas…

math.CV2023

Approximation and extension of Hermitian metrics on holomorphic vector bundles over Stein manifolds

Fusheng Deng, Jiafu Ning, Zhiwei Wang +1

We show that a singular Hermitian metric on a holomorphic vector bundle over a Stein manifold which is negative in the sense of Griffiths (resp. Nakano) can be approximated by a se…

math.CV2023

Degenerate complex Monge-Amp\` ere type equations on compact Hermitian manifolds and applications

Yinji Li, Zhiwei Wang, Xiangyu Zhou

We show the existence and uniqueness of bounded solutions to the degenerate complex Monge-Ampère type equations on compact Hermitian manifolds. We also study the asymptotics of the…

math.CV2022

Linear isometric invariants of bounded domains

Fusheng Deng, Jiafu Ning, Zhiwei Wang +1

We introduce two new conditions for bounded domains, namely $A^{p}$ -completeness and boundary blow down type, and show that, for two bounded domains $D_{1}$ and $D_{2}$ that are $A^{p}$ -co…

math.AG2022

Invariance of plurigenera for generalized polarized pairs with abundant nef parts

Zhan Li, Zhiwei Wang

We show the invariance of plurigenera for generalized polarized pairs with abundant nef parts and generalized canonical singularities. This is obtained by investigating a type of n…

math.CV2022★ 2 cited

On a Bogomolov type vanishing theorem

Zhi Li, Xiangkui Meng, Jiafu Ning +2

Let $X$ be a compact Kähler manifold and $(L, h) \to X$ be a pseudoeffective line bundle, such that the curvature $i Θ_{L, h} \geq 0$ in the sense of currents. The main result o…

math.CV2021

On the extension of Kähler currents on compact Kähler manifolds: holomorphic retraction case

Jiafu Ning, Zhiwei Wang, Xiangyu Zhou

In the present paper, we show that given a compact Kähler manifold $(X, ω)$ with a Kähler metric $ω$ , and a complex submanifold $V \subset X$ of positive dimension, if $V$ has a holo…

math.CV2020★ 1 cited

On the extensions of Kähler currents on compact Kähler manifolds

Zhiwei Wang, Xiangyu Zhou

Let $(X, ω)$ be a compact Kähler manifold with a Kähler form $ω$ of complex dimension $n$ , and $V \subset X$ is a compact complex submanifold of positive dimension $k < n$ . Suppose tha…

math.CV2020★ 10 cited

Positivity of holomorphic vector bundles in terms of $L^{p}$ -conditions of $\partial ˉ$

Fusheng Deng, Jiafu Ning, Zhiwei Wang +1

We study the positivity properties of Hermitian (or even Finsler) holomorphic vector bundles in terms of $L^{p}$ -estimates of $\partial ˉ$ and $L^{p}$ -extensions of holomorphic objec…

math.CV2019

Characterizations of plurisubharmonic functions

Fusheng Deng, Jiafu Ning, Zhiwei Wang

We give characterizations of (quasi-)plurisubharmonic functions in terms of $L^{p}$ -estimates of $\partial ˉ$ and $L^{p}$ -extensions of holomorphic functions.

math.CV2019★ 2 cited

Asymptotic estimate of cohomology groups valued in pseudo-effective line bundles

Zhiwei Wang, Xiangyu Zhou

In this paper, we study questions of Demailly and Matsumura on the asymptotic behavior of dimensions of cohomology groups for high tensor powers of (nef) pseudo-effective line bund…

math.CV2019★ 1 cited

CR eigenvalue estimate and Kohn-Rossi cohomology

Zhiwei Wang, Xiangyu Zhou

Let $X$ be a compact connected CR manifold with a transversal CR $S^{1}$ -action of real dimension $2 n - 1$ , which is only assumed to be weakly pseudoconvex. Let $□_{b}$ be the $\overl…

math.CV2019★ 3 cited

Linear invariants of complex manifolds and their plurisubharmonic variations

Fusheng Deng, Zhiwei Wang, Liyou Zhang +1

For a bounded domain $D$ and a real number $p > 0$ , we denote by $A^{p} (D)$ the space of $L^{p}$ integrable holomorphic functions on $D$ , equipped with the $L^{p}$ - pseudonorm. We prove th…

math.CV2018

A new proof of Kiselman's minimum principle for plurisubharmonic functions

Fusheng Deng, Zhiwei Wang, Liyou Zhang +1

We give a new proof of Kiselman's minimum principle for plurisubharmonic functions, based on Ohsawa-Takegoshi extension theorem.

math.CV2018★ 20 cited

New characterizations of plurisubharmonic functions and positivity of direct image sheaves

Fusheng Deng, Zhiwei Wang, Liyou Zhang +1

We give new characterizations of plurisubharmonic functions and Griffiths positivity of holomorphic vector bundles with singular Finsler metrics. As applications, we present a diff…

math.CV2017★ 1 cited

Local Demailly-Bouche's holomorphic Morse inequalities

Zhiwei Wang

Let $(X, ω)$ be a Hermitian manifold and let $(E, h^{E})$ , $(F, h^{F})$ be two Hermitian holomorphic line bundle over $X$ . Suppose that the maximal rank of the Chern curvature $c (E)$ of $…

math.DG2017★ 1 cited

On the volume of a pseudo-effective class and semi-positive properties of the Harder-Narasimhan filtration on a compact Hermitian manifold

Zhiwei Wang

This paper divides into two parts. Let $(X, ω)$ be a compact Hermitian manifold. Firstly, if the Hermitian metric $ω$ satisfies the assumption that $\partial\overline{\partial}ω^k=0…

math.CV2013

Bergman kernels and eigenvalue estimate of $\partial ˉ$ -laplacian

Zhiwei Wang

Let $(X, ω)$ be a compact Kähler manifold. Let $(L, h)$ be a hermitian holomorphic line bundle over $X$ , such that $Θ_{L, h} \geq - ε ω$ for a small $ε > 0$ , $E$ be a h…

On the extension of Kähler currents on compact complex manifolds

Capacity Stability of Complex Monge-Ampère Equations with Moving Prescribed Singularities

Macaulay representation of the prolongation matrix and the SOS conjecture

Log truncated threshold and zero mass conjecture

On the Range of a class of Complex Monge-Ampère operators on compact Hermitian manifolds

A note on Demailly's transcendental Morse inequalities conjecture

Approximation and extension of Hermitian metrics on holomorphic vector bundles over Stein manifolds

Degenerate complex Monge-Amp\` ere type equations on compact Hermitian manifolds and applications

Linear isometric invariants of bounded domains

Invariance of plurigenera for generalized polarized pairs with abundant nef parts

On a Bogomolov type vanishing theorem

On the extension of Kähler currents on compact Kähler manifolds: holomorphic retraction case

On the extensions of Kähler currents on compact Kähler manifolds

Positivity of holomorphic vector bundles in terms of Lp-conditions of ∂ˉ

Characterizations of plurisubharmonic functions

Asymptotic estimate of cohomology groups valued in pseudo-effective line bundles

CR eigenvalue estimate and Kohn-Rossi cohomology

Linear invariants of complex manifolds and their plurisubharmonic variations

A new proof of Kiselman's minimum principle for plurisubharmonic functions

New characterizations of plurisubharmonic functions and positivity of direct image sheaves

Local Demailly-Bouche's holomorphic Morse inequalities

On the volume of a pseudo-effective class and semi-positive properties of the Harder-Narasimhan filtration on a compact Hermitian manifold

Bergman kernels and eigenvalue estimate of ∂ˉ-laplacian

Positivity of holomorphic vector bundles in terms of $L^{p}$ -conditions of $\partial ˉ$

Bergman kernels and eigenvalue estimate of $\partial ˉ$ -laplacian