伪Hermitian流形上Hessian算子的精确全局界

紧致Hermitian流形上复Hessian方程的狄利克雷问题

The Dirichlet problem for a complex Hessian equation on compact Hermitian manifolds with boundary

利用$\bC^n$求解了小球上一般复Hessian方程的经典狄利克雷问题.然后，我们证明了具有局部共形Kähler度量边界的紧致Hermitian流形上的狄利克雷问题在多位势理论意义下存在连续解，并给出了一个子解.

Second order estimates for complex Hessian equations on Hermitian manifolds

We derive second order estimates for $χ$-plurisubharmonic solutions of complex Hessian equations with right hand sides depending on gradients on compact Hermitian manifolds.

Hermitian流形上Hessian方程的χ-半凸解的二阶估计

Second order estimates for $χ$-semi convex solutions of Hessian equations on Hermitian manifolds

本文在Hermitian流形上，针对方程两边含梯度项的复Hessian方程，利用半凸性假设建立修正凹性不等式，从而获得可容许解的二阶估计。

关于背景Hermitian形式的复Hessian测度

Complex Hessian measures with respect to a background Hermitian form

本文研究了关于背景Hermitian形式的复Hessian测度，发展了相关势理论，并扩展了复Hessian方程的研究结果。

埃尔米特流形上复赫斯方程的正则化与赫尔德连续性

Regularization and Hölder continuity for complex Hessian equations on Hermitian manifolds

针对紧埃尔米特流形上的复赫斯方程，提出$\u0393$-容许函数的定量正则化方法，证明右端项$L^p$（$p>\frac{n}{m}$）的复$m$-赫斯方程解的赫尔德连续性，并将结果推广至满足特定结构条件的一般类方程。

关于闭Hermitian流形上复椭圆型方程的一致估计

On uniform estimate of complex elliptic equations on closed Hermitian manifolds

本文研究了闭Hermitian流形上的Hessian方程和复商方程。我们直接导出了可采纳解的一致估计。作为应用，我们求解了闭Kähler流形上的一般Hessian方程.

Fully nonlinear elliptic equations with gradient terms on compact almost Hermitian manifolds

In this paper, we establish second order estimates for a general class of fully nonlinear equations with linear gradient terms on compact almost Hermitian manifolds. As an application, we first prove the existence of solutions for the Monge-Ampère equation with linear gradient terms for $(n-1)$-plurisubharmonic functions, originated from Gaudochon conjecture, in the almost Hermitian setting. Second, we solve the Monge-Ampère equation and Hessian equations with linear gradient terms. Third, we give the $C^{\infty}$ a priori estimates for the deformed Hermitian-Yang-Mills equation with supercrit…

Fully non-linear elliptic equations on compact almost Hermitian manifolds

In this paper, we establish a priori estimates for solutions of a general class of fully non-linear equations on compact almost Hermitian manifolds. As an application, we solve the complex Hessian equation and the Monge--Ampère equation for $(n-1)$-plurisubharmonic equations in the almost Hermitian setting.

厄米流形上完全非线性椭圆方程的稳定性与梯度估计

Stability and gradient estimates for fully nonlinear elliptic equations on hermitian manifolds

本文针对紧致厄米流形上的凹完全非线性椭圆方程，提出一种不依赖Hou-Ma-Wu估计和Liouville定理的梯度估计直接证明方法，并结合稳定性估计与比较论证，同时给出紧致Kähler流形上复Hessian估计的独立证明。

$m$-伪凸流形上复Hessian算子的特征值问题

The Eigenvalue Problem for the Complex Hessian Operator on $m$-Pseudoconvex Manifolds

本文研究强$m$-伪凸流形上复Hessian算子的特征值问题，证明了第一特征函数的$C^{1,1}$正则性与唯一性，并给出第一特征值的变分公式，进而推导出分岔型定理和几何界。

紧致Hermitian流形上复Hessian方程的一致\(L^\infty\)估计

Uniform $L^\infty$ estimates for complex hessian equations on compact Hermitian manifolds

研究紧致Hermitian流形上复Hessian方程，通过开发多重势方法，结合弱比较原理、容量理论及非线性迭代方案，在\(f \in L^p\)且\(f \ge 0\)（\(p>1\)）时给出一致\(L^\infty\)估计，并得到相关弱解结果，扩展了该理论。

关于紧致殆 Hermitian 流形上完全非线性椭圆方程的一个注记

A remark for fully non-linear elliptic equations on compact almost Hermitian manifolds

本文推广 sub-slope 定义至殆 Hermitian 流形，证明一类完全非线性椭圆方程解的存在性，并应用于复 Hessian 商方程和形变 Hermitian-Yang-Mills 方程。

完全非线性椭圆方程的上斜率和子解

Sup-slopes and sub-solutions for fully nonlinear elliptic equations

本文通过引入解析斜率不变量，给出闭黎曼或埃尔米特流形上一般完全非线性椭圆方程可解的充要条件，解决了Li-Urbas公开问题，并应用于求解非常数J-方程。

复Hessian商方程的粘性解

Viscosity solution to complex Hessian quotient equations

本文证明了紧致Hermitian流形上复Hessian方程在粘性意义下存在严格下解时粘性解的存在性，结果涵盖复Hessian商方程，推广了以往需满足行列式支配条件的研究。

完备非紧伪厄米流形上CR热方程的梯度估计

Gradient Estimates For The CR Heat Equation On Complete noncompact Pseudo-Hermitian Manifolds

本文在完备非紧伪厄米流形上建立CR热方程正解的Li-Yau型梯度估计，并由此导出Harnack不等式及热核上界估计。

闭黎曼流形上一般 $p$-Hessian 方程的 $\u200b\u200bC^2$ 估计

$\mathrm{C}^2$ estimates for general $p$-Hessian equations on closed Riemannian manifolds

本文针对闭黎曼流形上一般 $p$-Hessian 方程，引入伪解概念，在无曲率、凸性或 MTW 条件下证明了 $p\in\{2,n-1,n\}$ 时的 $C^1$ 与 $C^2$ 估计，并给出相关先验估计结论。

Parabolic complex Monge-Ampère equations on compact Hermitian manifolds

We prove the long-time existence and convergence of solutions to a general class of parabolic equations, not necessarily concave in the Hessian of the unknown function, on a compact Hermitian manifold. The limiting function is identified as the solution of an elliptic complex Monge-Ampère equation.