arXiv subjects
Publications and source records attributed to Ninh Van Thu.
The purpose of this article is twofold. First, we prove that the squeezing function approaches 1 near strongly pseudoconvex boundary points of bounded domains in $\mathbb{C}^{n+1}$. Second, we show that the squeezing function approaches 1 along certain sequences converging to pseudoconvex boundary points of finite type, including uniformly $Λ$-tangential and spherically $\frac{1}{2m}$-tangential convergence patterns.
In this paper, we present an explicit description for the boundary behavior of the Bergman kernel function, the Bergman metric, and the associated curvatures along certain sequences converging to an $h$-extendible boundary point.
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.
The principal eigenvalue for linear elliptic operator has been known to be one of very useful tools to investigate many important partial differential equations. Due to the pioneering works of Berestycki et al. \cite{BCV1,BCV2}, the study of qualitative properties for the principal eigenvalue of nonlocal operators has attracted a lot of attention of the community from theory to application (For examples \cite{LL22-1,LLS22,LZ1,LZ2,SLLY,DDF,XLR}). In this paper, motivated from the study of mathematical modeling the dynamics of infectious diseases in \cite{NV1, ZZLD, WD}, we analyze the asymptotic properties of the principal eigenvalue of nonlocal inhomogeneous cooperative system with respect to the dispersal rate and dispersal range. This can be done thanks to the deep results of Rainer \cite{Ra13}, Kriegl and Michor \cite{KM03} on the stability of eigenvalue of the variable matrices of zero-order coefficients and extends many results from \cite{BCV1,LL,NV1}. Our work provides a fundamental step to investigate the nonlinear system modeling the spreading of the transmitted diseases as mentioned.
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.
The purpose of this article is to investigate a hyperbolic complex manifold $M$ exhausted by a pseudoconvex domain $Ω$ in $\mathbb C^n$ via an exhausting sequence $\{f_j\colon Ω\to M\}$ such that $f_j^{-1}(a)$ converges to a boundary point $ξ_0 \in \partial Ω$ for some point $a\in M$.
In this paper, we prove that the general ellipsoid $D_P$ is holomorphically homogeneous regular provided that it is a $WB$-domain. Then, the uniform lower bound for the squeezing function near a $(P,r)$-extreme point is also given.
The purpose of this article is to prove that there exists a real smooth pseudoconvex hypersurface germ $(M,p)$ of D'Angelo infinite type in $\mathbb C^{n+1}$ such that it does not admit any (singular) holomorphic curve in $\mathbb C^{n+1}$ tangent to $M$ at $p$ to infinite order.
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.
Let $Ω$ be a pseudoconvex domain in $\mathbb C^n$ satisfying an $f$-property for some function $f$. We show that the Bergman metric associated to $Ω$ has the lower bound $\tilde g(δ_Ω(z)^{-1})$ where $δ_Ω(z)$ is the distance from $z$ to the boundary $\partialΩ$ and $\tilde g$ is a specific function defined by $f$. This refines Khanh-Zampieri's work in \cite{KZ12} with reducing the smoothness assumption of the boundary.
In this paper, we consider the following general evolution equation $$ u_t=Δ_fu+au\log^αu+bu $$ on smooth metric measure spaces $(M^n, g, e^{-f}dv)$. We give a local gradient estimate of Souplet-Zhang type for positive smooth solution of this equation provided that the Bakry-Émery curvature bounded from below. When $f$ is constant, we investigate the gereral evolution on compact Riemannian manifolds with no nconvex boundary satisfying an "\emph{interior rolling $R$-ball}" condition. We show a gradient estimate of Hamilton type on such manifolds.
In this paper, we prove Huang et al.'s conjecture stated that if $f$ is a holomorphic function on $Δ^+:=\{z\in \mathbb C \colon |z|<1,~\mathrm{Im}(z)>0\}$ with $\mathcal{C}^\infty$-smooth extension up to $(-1,1)$ such that $f$ maps $(-1,1)$ into a cone $Γ_C:=\{z\in \mathbb C\colon |\mathrm{Im} (z)| \leq C|\mathrm{Re} (z)|\}$, for some positive number $C$, and $f$ vanishes to infinite order at $0$, then $f$ vanishes identically. In addition, some regularity properties of the Riemann mapping functions on the boundary and an example concerning Huang et al.'s conjecture are also given.
We prove here the Wolff-Denjoy-type theorem for a very large class of pseudoconvex domains in $\mathbb C^n$ that may contain many classes of pseudoconvex domains of finite type and infinite type.
In this article, we consider an infinite type domain $Ω_P$ in $\mathbb C^2$. The purpose of this paper is to investigate the holomorphic vector fields tangent to an infinite type model in $\mathbb C^2$ vanishing at an infinite type point and to give an explicit description of the automorphism group of $Ω_P$.
The purpose of this paper is to give explicit descriptions for stability groups of real rigid hypersurfaces of infinite type in $\mathbb C^2$. The decompositions of infinitesimal CR automorphisms are also given.
In this note, we consider models in $\mathbb C^2$. The purpose of this note is twofold. We first show a characterization of models in $\mathbb C^2$ by their noncompact automorphism groups. Then we give an explicit description for automorphism groups of models in $\mathbb C^2$.
The purpose of this article is to investigate the holomorphic vector fields tangent to a real hypersurface in $\mathbb C^2$ vanishing at an infinite type point.