arXiv subjects
Publications and source records attributed to Nguyen Quang Dieu.
In this paper, we study Hessian type equations for $m-ω$ subharmonic functions. Using the recent results in \cite{KN23a}, \cite{KN23b}, we are able to show the existence of bounded solutions for such equations on bounded domains in $\mathbb{C}^n$.
In this paper, we study Hessian type equations for $(ø,m)-β$-subharmonic functions on a ball in $\mathbb{C}^n$, where $β=dd^c\|z\|^2=\frac{i}{2}\sum\limits_{j=1}^n dz_j\w d\bar{z}_j$ is the flat metric on $\cn$. Using the recent results in \cite{KN23b}, we are able to show the existence of bounded solutions for Hessian type equations.
In this paper, we concern with the existence of solutions of the complex $m-$Hessian type equation $-χ(u)H_{m}(u)=μ$ in the class $\mathcal{E}_{m,χ}(f,Ω)$ if there exists subsolution in this class, where the given boundary value $f\in\mathcal{N}_m(Ω)\cap MSH_m(Ω).$
In this paper, we first study subextensions in the classes $\mathcal{F}_{m}(Ω)$ and $\mathcal{E}_{m,χ}(Ω)$. These results are then used to study approximation in the classes $\mathcal{F}_{m}(Ω)$ and $\mathcal{E}_{m,χ}(Ω)$.
The purpose of this article is twofold. The first aim is to characterize an $n$-dimensional hyperbolic complex manifold $M$ exhausted by a sequence $\{Ω_j\}$ of domains in $\mathbb C^n$ via an exhausting sequence $\{f_j\colon Ω_j\to M\}$ such that $f_j^{-1}(a)$ converges to a boundary point $ξ_0 \in \partial Ω$ for some point $a\in M$. Then, our second aim is to show that any spherically extreme boundary point must be strongly pseudoconvex.
In this paper, we first study the comparison principle for the operator $H_{χ,m}$. This result is used to solve certain weighted complex $m-$ Hessian equations.
The purpose of this article is twofold. The first aim is to prove that if there exist a sequence $\{φ_j\}\subset \mathrm{Aut}(Ω)$ and $a\in Ω$ such that $\lim_{j\to\infty}φ_j(a)=ξ_0$ and $\lim_{j\to\infty}σ_Ω(φ_j(a))=1$, where $ξ_0$ is a linearly convex boundary point of finite type, then $ξ_0$ must be strongly pseudoconvex. Then, the second aim is to investigate the boundary behaviour of the squeezing function of a general ellipsoid.
In this paper, we characterize weakly pseudoconvex domains of finite type in $\mathbb C^n$ in terms of the boundary behavior of automorphism orbits by using the scaling method.
We investigate decay near boundary of the volume of sublevel sets in Cegrell classes of $m-$ subharmonic function on bounded domains in $\mathbb C^n.$ On the reverse direction, some sufficient conditions for membership in certain Cegrell's classes, in terms of the decay of the sublevel sets, are also discussed.
The purpose of this article is twofold. The first aim is to characterize $h$-extendibility of smoothly bounded pseudoconvex domains in $\mathbb C^{n+1}$ by their noncompact automorphism groups. Our second goal is to show that if the squeezing function tends to $1$ at an $h$-extendible boundary point of a smooth pseudoconvex domain in $\mathbb C^{n+1}$, then this point must be strongly pseudoconvex.
We give upper bounds for volume of sublevel sets of real polynomials. Our method is to combine a version of global Lojasiewicz inequality with some well known estimate on volume of tubes around real algebraic sets. Some applications to oscillatory integrals and integration indices of real polynomial are also given.
Let $D$ be a bounded domain in $\mathbb C^n$. We study approximation of (not necessarily bounded from above) $m-$subharmonic function $D$ by continuous $m-$subharmonic ones defined on neighborhoods of $\overline{D}$. We also consider the existence of a $m-$subharmonic function on $D$ whose boundary values coincides with a given real valued continuous function on $\partial D$ except for a sufficiently small subset of $\partial D.$
The main goal of this article is to find, following the approach given in [Ce1] and [Ce2], the largest possible sub-class of plurisubharmornic functions on a complex variety on which the complex Monge-Ampère operator can be reasonably defined. Moreover, we are also interested in giving sufficient condition for solvability of the Monge-Ampère operator Monge-Ampère operators on complex varieties.
We prove a strong version of the comparison principle for bounded plurisubharmonic function on complex varieties. we then apply our main result to study convergence of Mong-Ampere mesures for bounded plurisubharmonic functions.
We discuss possible generalizations of Vitali convergence theorem when the source and the target are Banach analytic manifolds. These results are then applied to study behavior of holomorphic mappings between Banach analytic manifolds. Explicit examples of manifolds having Vitali properties are also provided.
We prove some results which give sufficient conditions so that pointwise approximation of negative plurisubharmonic functions on complex varieties by continuous plurisubharmonic ones is possible.
Let $\Om$ be a unbounded domain in a Banach space. In this work, we wish to impose {\it local conditions} on boundary point of $\Om$ (including the point at infinity) that guarantee complete hyperbolic of $\Om.$ We also search for local boundary conditions so that Vitali properties hold true for $\Om.$ These properties might be considered as analogues of the taut property in the finite dimensional case.
We find the precise growth of some invariant metrics near a point on the boundary of a domain where the Levi form has at least one negative eigenvalue. We also introduce a new invariant pseudometric which is convenient in this context, and give some of its general properties.