Hoang-Son Do, Thanh Cong Ngoc Pham
In this paper, we study the Cauchy-Dirichlet problem for Parabolic complex Monge-Ampère equations on strongly pseudoconvex domains using the viscosity method. We prove a comparison principle for Parabolic complex Monge-Ampère equations and use it to study the existence and uniqueness of viscosity solution in certain cases where the sets $\{z\inΩ: f(t, z)=0 \}$ may be pairwise disjoint.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Weak solution of Parabolic complex Monge-Ampére equation II
研究了\mathbb{C}^n中有界严格拟凸区域上抛物型复Monge-Ampére方程，边界条件u=φ，初始条件u=u_0.本文考虑φ是光滑的，u_0是Ω的一个邻域内的任意多重次调和函数，满足u_0=φ（.，0)在Ω的边界上。
In this paper, we study the Cauchy-Dirichlet problem for Parabolic complex Monge-Ampère equations on a strongly pseudoconvex domain by the viscosity method. We extend the results in [EGZ15b] on the existence of solution and the convergence at infinity. We also establish the Hölder regularity of the solutions when the Cauchy-Dirichlet data are Hölder continuous.
Locally Monge-Ampere Foliations
证明了复流形的余维1抛物叶理是全纯的。这是证明使用的事实，余维1叶状的复流形必然是局部蒙赫安培叶状和抛物叶不能有双曲行为。结果也适用于局部Monge-Ampère叶理抛物叶任意余维。
Weak solution of Parabolic complex Monge-Ampère equation
本文研究了$\mathbb{C}^n$中定义域上的方程$\dot{u}=\log\det (u_{α\barβ})-Au+f(z,t)$.该方程与凯勒-里奇流有着密切的联系。本文考虑了边界条件是光滑的，初始条件是不规则的情形。
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.
We study the long-time existence and convergence of general parabolic complex Monge-Ampere type equations whose second order operator is not necessarily convex or concave in the Hessian matrix of the unknown solution.
In this paper, we consider a version of parabolic complex Monge-Ampere equations, and use a PDE approach similar to Phong et al to establish $L^{\infty}$ and Hölder estimates. We also generalize the $L^{\infty}$ estimates to parabolic Hessian equations.
The parabolic quaternionic Monge-Ampère type equation on hyperKähler manifolds
本文证明紧致超Kähler流形上抛物型四元数Monge-Ampère型方程解的长时存在唯一性，并证明归一化后光滑收敛到相应Monge-Ampère方程的唯一解。
A Decomposition of Complex Monge-Ampere Measures
证明了多重次调和函数的复Monge-Ampere测度与其多极集的一个分解定理。
Monge-Ampère operator on four dimensional almost complex manifolds
在四维殆复流形上定义了连续J-多重次调和函数的Monge-Ampère算子.
Complex Monge-Ampere of a Maximum
我们给出了复Monge-Ampere算子应用于有限个函数的最大值的一个公式。
We prove the Hölder continuity of the unique solution to quaternionic Monge-Ampère equation with densities in $L^{p},$ $p>2,$ on a bounded strictly pseudoconvex domains.
Monge-Ampère operators on complex varieties in $\C^n
本文的主要目标是找到，按照[Ce 1]和[Ce 2]中给出的方法，复簇上的pluisubharmornic函数的最大可能子类，复Monge-Ampère算子可以合理地定义。此外，我们还给出了复簇上的Monge-Ampère算子可解的充分条件.
On a Monge-Ampère type equation in the Cegrell class $\mathcal{E}_χ$
本文证明了Cegrell类$\mathcal{E}_χ$中一类Monge-Ampère型方程解的存在唯一性.
Some properties of the complex Monge-Ampere operator in Cegrell's classes and applications
本文首先证明一个关于容量收敛的结果。利用所得结果，我们将得到复Monge-Ampere测度的一个一般分解定理，该定理将用于证明复Monge-Ampere算子的一个比较原理.
Hölder continuous solutions to the complex Monge-Ampère equations in non-smooth pseudoconvex domains
本文证明了复蒙日-安培方程在多重次调和型${m}$的非光滑拟凸域上解的Hölder连续性.
An Inequality for Mixed Monge-Ampère measures
本文推广了混合Monge-Ampère测度的一个不等式。我们还给出了一个例子，表明我们的假设是尖锐的。在紧Kähler流形的情形下，也讨论了相应的结果.
On a Monge-Ampère operator for plurisubharmonic functions with analytic singularities
研究了具有解析奇点的多重次调和函数的广义Monge-Ampère算子的连续性.特别是，我们证明了连续性的自然类减少逼近序列。我们还证明了一个公式的总质量的Monge-Ampère措施，这样的功能，在一个紧凑的Kähler流形。
We give a sufficient condition on a sequence of uniformly bounded $ω$-plurisubharmonic functions, $ω$ being a Hermitian metric, for which the sequence of associated Monge-Ampère measures converges weakly. This criterion can be used to obtained a bounded $ω$-plurisubharmonic solution to the Monge-Ampère equation.
In this paper, we are interested in studying the Dirichlet problem for the complex Monge-Ampère operator. We provide necessary and sufficient conditions for the problem to have Hölder continuous solutions.
Monge-Ampere measures on pluripolar sets
本文对具有大奇异部分测度的复Monge-Ampere方程进行了求解。这个结果推广了Demailly，Lelong和Lempert等人的经典结果，他们认为奇异部分是离散集。利用我们的结果得到了Kolodziej下解定理的一个推广。更确切地说，我们证明了，如果一个非负Borel测度是由一个复杂的Monge-Ampere测度支配，那么它是一个复杂的Monge-Ampere测度。
Higher Lelong numbers versus full Monge-Ampère mass
本研究证明了Chi Li提出的关于高阶Lelong数与满Monge-Ampère质量关联的猜想，推进了相关复分析理论研究。
This paper studies the complex Monge-Ampère equations for $\mathcal F$-plurisubharmonic functions in bounded $\mathcal F$-hyperconvex domains. We give sufficient conditions for this equation to solve for measures with a singular part.
Stability of Bounded Solutions for Degenerate Complex Monge-Ampère equations
本文推广和加强了Kokodziej的稳定性定理。特别地，我们给出了精确的稳定性指数，并处理了蒙日-安培方程右端奇异性更强的情形.
A local regularity for the complex Monge-Ampère equation
本文证明了非退化复Monge-Ampére方程多重次调和解的局部正则性（以及相应的先验估计），假定其$W^{2,p}$ -范数是在某些$p>n(n-1)$的控制下.这个条件是最佳的。我们特别使用的一些方法开发的Trudinger和$L^q$ -估计复杂的蒙赫-安培方程由于Kokudziej。
Regularity of push-forward of Monge-Amp{è}re measures
证明了H{<$}lder连续拟psh函数的Monge-Pére测度在任意支配亚纯映射下的象仍具有H{<$}lder势.我们还讨论了低正则性的情况。
The $\mathcal C^{2,α}$ estimate of complex Monge-Ampere equation
证明了复蒙日-安培方程$det(u_{i\bar{j}})=f$的任何$\mathcal C^{1,1}$解都是$α\in (0,1)$的$0<f\in\mathcal C^α$在$\mathcal C^{2,α}$中.
On the Hölder continuous subsolution problem for the complex Monge-Ampère equation
给出了正Borel测度使得复蒙日-安培方程的狄利克雷问题在零边界条件下存在Hölder连续多重次调和解的充要条件.特别地，当子解具有有限的Monge-Ampère总质量时，我们对Zeriahi的一个问题得到了肯定的回答。
We show that the Monge-Ampère density of the extremal function $V_P$ for a non-convex Pac-Man set $P\subset {\bf R}^2$ tends to a finite limit as we approach the vertex $p$ of $P$ linearly but with a value that may vary with the line. On the other hand, along a tangential approach to $p$ the Monge-Ampère density becomes unbounded. This partially mimics the behavior of the Monge-Ampère density of the union of two quarter disks set $S$ of Sigurdsson and Snaebjarnarson. We also recover their formula for $V_S$ by elementary methods.
Cegrell classes and a variational approach for the quaternionic Monge-Ampere equation
本文在H_n的四元数超凸区域上引入了Cegrell型四元数多重次调和函数的有限能量类，并研究了这些能量类上的四元数Monge-Ampere算子.本文将四元数Monge-Ampere算子的定义域推广到某些函数不一定有界的Cegrell类上。证明了分部积分法和比较原理在某些类上是有效的。此外，我们还用变分方法求解了四元数的Monge-Ampere方程，当方程的右端为有限能量的正测度时.
Monge-Ampere measures on subvarieties
本文讨论复蒙日-安培方程对于具有大奇异部分的测度是否可解的问题。我们证明了在某些条件下，当右端为$k<n$维的$\CEP{n}$中的光滑子簇时，方程无解.
Complex Monge-Ampère equation in strictly pseudoconvex domains
研究了严格拟凸区域$Ω$中的复蒙日-安培方程$(dd^c u)^n=μ$，边界条件为$u=φ$，其中$φ\in C(\partialΩ)$ .给出了解$u$在“小集合”外连续的非平凡充分条件。
On the Maximal Rank Problem for the Complex Homogeneous Monge-Ampère Equation
我们给出了单位圆盘上的复齐次蒙日-安培方程的狄利克雷问题的正则边界数据的例子，其解在非空开集上完全退化，因此没有最大秩。
Many fundamental results of pluripotential theory on the quaternionic space $\mathbb{H}^n$ are extended to the Heisenberg group. We introduce notions of a plurisubharmonic function, the quaternionic Monge-Ampère operator, differential operators $d_0$ and $d_1$ and a closed positive current on the Heisenberg group. The quaternionic Monge-Ampère operator is the coefficient of $ (d_0d_1u)^n$. We establish the Chern-Levine-Nirenberg type estimate, the existence of quaternionic Monge-Ampère measure for a continuous quaternionic plurisubharmonic function and the minimum principle for the quaternioni…
We develop the first steps of a parabolic pluripotential theory in bounded strongly pseudo-convex domains of Cn. We study certain degenerate parabolic complex Monge-Amp{è}re equations, modelled on the K{ä}hler-Ricci flow evolving on complex algebraic varieties with Kawamata log-terminal singularities. Under natural assumptions on the Cauchy-Dirichlet boundary data, we show that the envelope of pluripotential subsolutions is semi-concave in time and continuous in space, and provides the unique pluripotential solution with such regularity.
Weak solutions to degenerate complex Monge-Ampére flows I
研究里奇流在轻度奇异簇上的（长期）行为，自然会导致退化抛物型复Monge-Ampére方程的弱解的研究。本文是关于这个问题的系列文章中的第一篇，目的是发展$\C^n$域中退化复Monge-Ampère流的粘性理论。
Regularity of A Complex Monge-Ampère Equation on Hermitian Manifolds
我们得到了紧致Hermitian流形上抛物流的高阶估计。作为应用，我们证明了椭圆型复蒙日-安培方程的有界$\hatω$ -多重次调和解在背景厄米度量$\hatω$的假设下是光滑的.这推广了Székelyhidi和Tosatti关于Kähler流形的一个结果。
Weak subsolutions to complex Monge-Ampère equations
我们比较了退化复蒙日-安培方程的弱下解的各种概念，表明它们都是一致的。这使我们能够给出另一种证明混合蒙日安培不等式由于Kolodziej和Dinew。
Subsolution theorem and the Dirichlet problem for the quaternionic Monge-Ampere equation
本文研究了四元数蒙日-安培方程，在严格伪凸区域上得到了这类方程的狄利克雷问题解的存在性.建立了四元数蒙日-安培方程的稳定性和下解定理.
Weak Solutions To Complex Monge-Ampère Equation on hyperconvex domains
给出了超凸域上复Monge-Ampère型方程的一个非常一般的存在性定理。
Continuity of the Complex Monge-Ampere Operator on Compact Kahler Manifolds
证明了复Monge-Ampere算子在紧致Kahler流形上的几个逼近定理。作为应用，我们给出了Guedj和Zeriahi关于复Monge-Ampere算子在复Monge-Ampere质量为零的w-多重次调和函数类中的值域的一个新的证明.作为副产品，我们得到了复Monge-Ampere方程在某些子类中解的稳定性定理。
We establish a stability result for elliptic and parabolic complex Monge-Amp{è}re equations on compact K{ä}hler manifolds, which applies in particular to the K{ä}hler-Ricci flow. Dedicated to Jean-Pierre Demailly on the occasion of his 60th birthday.
We solve the Dirichlet Problem of Monge-Ampère equation near an isolate Klt singularity, which generalizes the result of Eyssidieux-Guedj-Zeriahi \cite{EGZ}, where the Monge-Ampère equation is solved on singular varieties without boundary. As a corollary, we construct solutions to Monge-Ampère equation with isolated singularity on strongly pseudoconvex domain $Ω$ contained in $\mathbb{C}^n$.
Weak Solutions to Complex Monge-Ampère Equations on Compact Kähler Manifold
给出了紧致Kähler流形上复Monge-Ampère型方程的一个普遍存在性定理.
Envelope Approach to Degenerate Complex Monge-Ampère Equations on compact Kähler manifold
我们将利用经典的Perron包络方法证明紧致Kähler流形上退化复Monge-Ampère型方程的一般存在性定理。
The Monge-Ampère equation on almost complex manifolds
研究了殆复流形上蒙日-安培方程的狄利克雷问题.在严格伪凸区域上，我们得到了该问题的唯一光滑解的存在性。
On Degenerated Monge-Ampere Equations over Closed Kähler Manifolds
本文研究了具有退化上同调类的闭Kähler流形上的Monge-Ampere方程。对多能理论中的经典结果和论点进行了一点推广，使之适用于我们的情况。
Let $(X,ω)$ be a compact Kähler manifold. We prove that all Monge-Ampère capacities are comparable. Using this we give an alternative direct proof of the integration by parts formula for non-pluripolar products recently proved by M. Xia.
We show that a positive Borel measure of positive finite total mass, on compact Hermitian manifolds, admits a Holder continuous quasi-plurisubharmonic solution to the Monge-Ampere equation if and only if it is dominated locally by Monge-Ampere measures of Holder continuous plurisubharmonic functions.
Monge-Ampere foliations for degenerate solutions
研究了复齐次蒙日-安培方程在任意退化点上的多重次调和解所对应的Monge-Ampère叶理的存在性和全纯性问题.对于实解析无界解，我们得到了很好的结果。因此，我们也提供了一个肯定的答案，伯恩斯的一个问题的齐次多项式，其对数满足复杂的蒙日-安培方程，我们得到了推广的工作P.M.黄完全加权圆形域的分类。
The complex Monge-Ampère equation on compact Hermitian manifolds
我们表明，到缩放，紧凑的埃尔米特流形上的复杂的蒙格-安培方程总是承认一个光滑的解决方案。
We prove the bounded subsolution theorem for the complex Monge-Ampère type equation, with the right hand side being a positive Radon measure, on a compact Hermitian manifold with boundary.
Hölder continuity of solutions to the complex Monge-Ampère equation with the right hand side in L^p. The case of compact Kähler manifolds
证明了在紧Kähler流形上，复蒙日-安培方程的解是Hölder连续的，其中右端在$L^p, p>1,$中.
Finite Type Monge-Ampère Foliations
本文将我们以前关于Monge-Ampère叶理的奇异性的工作推广到伪凸有限型域的情形。我们能够回答伯恩斯关于其对数完全满足2维复蒙日-安培方程的齐次多项式的问题。我们也能够推广的工作P. M. Wong在2维完全加权圆形域的分类，包括有限型域。
Monge-Ampère exhaustions of almost homogeneous manifolds
我们考虑了三类基本的紧几乎齐次流形，证明了这类流形中奇异复轨道的补空间具有满足复齐次蒙日-安培方程的多重次调和穷竭.这扩展到一个新的家庭的混合型的例子各种经典的结果抛物空间和复杂的对称空间。刚性结果的复杂空间建模这样的新的例子。
Domains of definition of Monge-Ampère operators on compact Kähler manifolds
设$(X,ω)$是紧致Kähler流形.引入并研究了复Monge-Ampère算子定义在其上的$ω$ -多重次调和（psh）函数的最大集合$DMA(X,ω)$.它比定义的相应局部域大得多，但仍然是所有$\om$ -psh函数的集合$PSH(X,\om)$的真子集。证明了某些扭曲的Monge-Ampère算子对所有$ω$ -psh函数都是好定义的.因此，任何具有轻微衰减奇点的$\om$ -psh函数都具有有限的加权Monge-Ampère能量。
Continuity of Monge-Ampère Potentials with Prescribed Singularities
本文研究带预定奇点的复 Monge-Ampère 方程解的连续性，推广了已有结果，并据此实现从预定奇点流启动 Monge-Ampère 流。
We characterize the class of probability measures on a compact Kahler manifold such that the associated Monge-Ampère equation has a solution of finite pluricomplex energy. Our results are also valid in the big cohomology class setting.
Generalized Monge-Ampère capacities
本文研究了紧Kähler流形上的各种容性，推广了Bedford-Taylor Monge-Ampère容性.然后我们利用这些能力来研究复蒙日-安培方程解的存在性和正则性。
The weigthed Monge-Ampère energy of quasiplurisubharmonic functions
研究紧致Kähler流形$(X,ω)$上退化的复蒙日-安培方程.证明了复Monge-Ampère算子$(ω+ dd^c \cdot)^n$在具有有限加权Monge-Ampère能量的$ω$ -多重次调和函数的类${\mathcal E}(X,ω)$上是良好定义的.类${\mathcal E}(X,ω)$是最大的一类$ω$ -psh函数，在它上面Monge-Ampère算子是定义良好的，比较原理是有效的。它包含几个梯度不是平方可积〔的〕。我们给出了一个完整的描述的范围内的Monge安培运营商$(ω+dd^c \cdot)^n$的${\mathcal E}(X,ω)$，以及对它的一些子类。我们还研究了唯一性的性质，扩展卡拉比的结果，这种无界和退化的情况下，我们给应用程序复杂的动力学和奇异凯勒-爱因斯坦度量的存在。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。