相关论文: The Diederich-Fornaess Index and Good Vector Field…

We study a geometric property of the boundary on Hartogs domains which can be used to find upper and lower bounds for the Diederich-Forn{\ae}ss Index. Using this, we are able to show that under some reasonable hypotheses on the set of…

We describe along the guidelines of Kohn "Quantitative estimates..." (1999), the constant E_s which is needed to control the commutator of a totally real vector field T with di-bar* in order to have Sobolev s-regularity of the Bergman…

Let $\Omega$ be a smooth bounded pseudoconvex domain in $\mathbb{C}^{n}$. Let $1\leq q_{0}\leq (n-1)$. We show that if $q_{0}$--sums of eigenvalues of the Levi form are comparable, then if the Diederich--Forn\ae ss index of $\Omega$ is $1$,…

We study bounded pseudoconvex domains in complex Euclidean spaces. We find analytical necessary conditions and geometric sufficient conditions for a domain being of trivial Diederich--Forn\ae ss index (i.e. the index equals to 1). We also…

We introduce the concept of Steinness index related to the Stein neighborhood basis. We then show several results: (1) The existence of Steinness index is equivalent to that of strong Stein neighborhood basis. (2) On the…

The Diederich--Forn\ae ss index has been introduced since 1977 to classify bounded pseudoconvex domains. In this article, we derive several intrinsic, geometric conditions on boundary of domains for arbitrary indexes. Many results, in the…

We derive a sufficient condition on a bounded pseudoconvex domain $\Omega\subset\mathbb{C}^2$ with smooth boundary such that $-(-\rho)^\eta$ is plurisubharmonic on $\Omega$ for $\eta>0$ arbitrarily close to $1$ (the supremum of $\eta$ is…

A sufficient condition for the infinite dimensionality of the Bergman space of a pseudoconvex domain is given. This condition holds on any pseudoconvex domain that has at least one smooth boundary point of finite type in the sense of…

We study bounded pseudoconvex domains in complex Euclidean space. We define an index associated to the boundary and show this new index is equivalent to the Diederich-Forn{\ae}ss index defined in 1977. This connects the…

A uniform upper bound for the Diederich--Fornaess index is given for weakly pseudoconvex domains whose Levi-form of the boundary vanishes in $\ell$-directions everywhere.

In this paper, we prove the semi-continuity theorem of Diederich-Forn{\ae}ss index and Steinness index under a smooth deformation of pseudoconvex domains in Stein manifolds.

We show, under an assumption on the weakly pseudoconvex points, the trivial Diederich--Forn\ae ss index directly implies the global regularities of the $\bar{\partial}$-Neumann operators.

We show that if the closure of a smooth pseudoconvex domain admits a "sufficiently nice" Stein neighborhood basis, then the d-bar Neumann problem on the domain is globally regular.

Let D be a smoothly bounded domain in a complex vector space of dimension n. Suppose that D has a smooth defining function, such that the sum of any q eigenvalues of its complex Hessian are non-negative on the closure of D. We show that…

Let $\Omega\subset \mathbb{C}^{n}$, with $n \geq 3$, be a smooth bounded pseudoconvex domain satisfying the symmetric eigenvalue comparability condition $D(q_0)$ for some $1\le q_0\le n-2$. We show that if the Diederich-Fornaess-index of…

We show that the Diederich-Fornaess index of a domain in a Stein manifold is invariant under CR-diffeomorphisms. For this purpose we also improve CR-extension theorem.

We propose the concept of Diederich--Forn{\ae}ss and Steinness indices on compact pseudoconvex CR manifolds of hypersurface type in terms of the D'Angelo 1-form. When the CR manifold bounds a domain in a complex manifold, under certain…

The purpose of this paper is to prove that if a pseudoconvex domains $\Omega\subset\mathbb{C}^n$ satisfies Bell-Ligocka's Condition R and admits a ``good" dilation, then the Bergman projection has local $L^p$-Sobolev and H\"older estimates.…

Yet another proof is given for a global estimate of the Diederich--Fornaess index of relatively compact domains with Levi-flat boundary, namely, the index must be smaller than or equal to the reciprocal of the dimension of the ambient…

We derive optimal estimates for the Bergman kernel and the Bergman metric for certain model domains in $\mathbb{C}^2$ near boundary points that are of infinite type. Being unbounded models, these domains obey certain geometric constraints…