相关论文: The Diederich--Forn\ae ss index and the regulariti…

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 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…

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…

This article chronicles a development that started around 1990 with \cite{BoasStraube91}, where the authors showed that if a smooth bounded pseudoconvex domain $\Omega$ in $\mathbb{C}^{n}$ admits a defining function that is plurisubharmonic…

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 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…

In the paper we give a lower estimate for the essential norm of the $\bar{\partial}$-Neumann operator on convex domains and worm domains of Diederich and Fornaess.

The $\bar{\partial}$-Neumann problem is the fundamental boundary value problem in several complex variables. It features an elliptic operator coupled with non-coercive boundary conditions. The problem is globally regular on many, but not…

We obtain weighted estimates for the $\bar{\partial}$-Neumann operator on intersections of two smooth strictly pseudoconvex domains in $\mathbb{C}^2$. The regularity estimates are described with the use of Sobolev norms with weights which…

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 establish general sufficient conditions for exact (and global) regularity in the $\bar\partial$-Neumann problem on $(p,q)$-forms, $0 \leq p \leq n$ and $1\leq q \leq n$, on a pseudoconvex domain $\Omega$ with smooth boundary $b\Omega$ in…

We consider the relationship between two sufficient conditions for regularity of the Bergman Projection on smooth, bounded, pseudoconvex domains. We show that if the set of infinite type points is reasonably well-behaved, then the existence…

For a domain $D$ of $\mathbb{C}^n$ which is weakly $q$-pseudoconvex or $q$-pseudoconcave we give a sufficient condition for subelliptic estimates for the $\bar{\partial}$-Neumann problem. The paper extends to domains which are not…

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 introduce a new geometrical invariant of CR manifolds of hypersurface type, which we dub the "Levi core" of the manifold. When the manifold is the boundary of a smooth bounded pseudoconvex domain, we show how the Levi core is related to…

A theory of global regularity of the d-bar-Neumann operator is developed which unifies the two principal approaches to date, namely the one via compactness due to Kohn-Nirenberg and Catlin, and the one via plurisubharmonic defining…

This thesis starts from a review on current research on the local hypoellipticity of the $\bar\partial$-Neumann problem. It presents the classical method of regularity from estimates of the energy: subelliptic as well as superlogarithmic.…

We prove that the $\bar\partial$-Neumann solution operator is locally regular in a domain which has compactness estimates, is of finite type outside a curve transversal to the CR directions and for which the holomorphic tangential…

For smooth bounded pseudoconvex domains in $mathbb{C}^{2}$, we provide geometric conditions on (the points of infinite type in) the boundary which imply compactness of the $\bar{\partial}$-Neumann operator. It is noteworthy that the proof…