Yulun Xu

activity

20192026

collaborators

11 papers

math.DG2026

Shrinking Kähler-Ricci solitons on toric fano fibrations

Tristan C. Collins, Genggeng Huang, Freid Tong +1

We prove that a smooth toric Fano fibration admits a complete gradient shrinking Kähler-Ricci soliton.

math.AP2026

Regularization and Hölder continuity for complex Hessian equations on Hermitian manifolds

Yulun Xu

Let $(M, ω)$ be a compact Hermitian manifold, and let $Γ$ be a symmetric convex cone. We develop a quantitative regularization method for $Γ$ -admissible functions. As an application…

math.DG2026

A numerical criterion for complex Hessian type equations on projective manifolds

Gao Chen, Sijie Nie, Yulun Xu

We prove a Nakai-Moishezon-type criterion for complex Hessian-type equations on projective manifolds whose associated degree- $n$ polynomials are strongly strictly right-Noetherian.…

math.DG2025

The uniqueness of Poincaré type extremal Kähler metric

Yulun Xu

Let $D$ be a smooth divisor on a closed Kähler manifold $X$ . Suppose that $A u t_{0} (D) = {I d}$ . We prove that the Poincaré type extremal Kähler metric with a cusp singularity at $D$ i…

math.AP2025

Viscosity solution to complex Hessian quotient equations

Jingrui Cheng, Yulun Xu

In this paper, we prove the existence of viscosity solutions to complex Hessian equations on compact Hermitian manifolds, assuming the existence of a strict subsolution in the visc…

math.DG2024

On the uniqueness of Poincaré type cscK metrics

Yulun Xu, Kai Zheng

Let $X$ be a compact Kähler manifold with a divisor $D$ which may have simple normal crossings. We prove that the $K$ -energy is convex on the space of Poincaré type Kähler metrics.…

math.AP2024

Viscosity solution to complex Hessian equations on compact Hermitian manifolds

Jingrui Cheng, Yulun Xu

We prove the existence of viscosity solutions to complex Hessian equations on a compact Hermitian manifold that satisfy a determinant domination condition. This viscosity solution…

math.CV2023

Interior Hölder estimate for the linearized complex Monge-Ampere equation

Yulun Xu

Let $w_{0}$ be a bounded, $C^{3}$ , strictly plurisubharmonic function defined on $B_{1} \subset C^{n}$ . Then $w_{0}$ has a neighborhood in $L^{\infty} (B_{1})$ . Suppose that we have a f…

math.AP2023

Interior $W^{2, p}$ estimate for small perturbations to the complex Monge-Ampere equation

Jingrui Cheng, Yulun Xu

Let $w_{0}$ be a bounded, $C^{3}$ , strictly plurisubharmonic function defined on $B_{1} \subset C^{n}$ . Then $w_{0}$ has a neighborhood in $L^{\infty} (B_{1})$ with the following proper…

math.AP2022

Regularization Of $m$ -subharmonic Functions And HÖlder Continuity

Jingrui Cheng, Yulun Xu

We use sup-convolution to find upper approximations of a bounded $m$ -subharmonic function on a compact Kähler manifold with nonnegative holomorphic bisectional curvature. As an app…

math.CO2019

The k-Power Domination Number in Some Self-Similar Graphs

Yulun Xu, Qi Bao, Zhongzhi Zhang

The $k$ -power domination problem is a problem in graph theory, which has applications in many areas. However, it is hard to calculate the exact $k$ -power domination number since de…

Shrinking Kähler-Ricci solitons on toric fano fibrations

Regularization and Hölder continuity for complex Hessian equations on Hermitian manifolds

A numerical criterion for complex Hessian type equations on projective manifolds

The uniqueness of Poincaré type extremal Kähler metric

Viscosity solution to complex Hessian quotient equations

On the uniqueness of Poincaré type cscK metrics

Viscosity solution to complex Hessian equations on compact Hermitian manifolds

Interior Hölder estimate for the linearized complex Monge-Ampere equation

Interior W2,p estimate for small perturbations to the complex Monge-Ampere equation

Regularization Of m-subharmonic Functions And HÖlder Continuity

The k-Power Domination Number in Some Self-Similar Graphs

Interior $W^{2, p}$ estimate for small perturbations to the complex Monge-Ampere equation

Regularization Of $m$ -subharmonic Functions And HÖlder Continuity