Related papers: Complex Manifolds In $Q$-Convex Boundaries

In this paper we deal with the following question: is it true that any bounded smooth pseudoconvex domain in $\mathbb{C}^n$ whose boundary contains a $q$-dimensional complex manifold $M$ necessarily has a noncompact…

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…

We prove local hypoellipticity of the complex Laplacian $\Box$ and of the Kohn Laplacian $\Box_b$ in a pseudoconvex boundary when, for a system of cut-off $\eta$, the gradient $\partial_b\eta$ and the Levi form…

Let \Omega be a bounded, weakly convex domain in C^n, n>1, having real-analytic boundary. A(\Omega) is the algebra of all functions holomorphic in \Omega and continuous upto the boundary. A submanifold M\subset \partial\Omega is said to be…

We consider a compact $n$-dimensional complex manifold endowed with a holomorphic line bundle that is semi-positive everywhere and positive at least at one point. Additionally, we have a smooth domain of this manifold whose Levi form has at…

Let $1\leq q\leq (n-1)$. We first show that a necessary condition for a Hankel operator on $(0,q-1)$-forms on a convex domain to be compact is that its symbol is holomorphic along $q$-dimensional analytic varieties in the boundary. Because…

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…

The Levi geometry at weakly pseudoconvex boundary points of domains in C^n, n \geq 3, is sufficiently complicated that there are no universal model domains with which to compare a general domain. Good models may be constructed by bumping…

Let $\Omega$ be a pseudoconvex domain with $C^2$-smooth boundary in $\mathbb CP^n$. We prove that the $\bar\partial-Neumann operator $N$ exists for $(p,q)$-forms on $\Omega$. Furthermore, there exists a $t_0>0$ such that the operators $N$,…

Let $\Omega$ be a pseudoconvex domain in $\mathbb C^n$ with smooth boundary $b\Omega$. We define general estimates $(f\text{-}\mathcal M)^k_{\Omega}$ and $(f\text{-}\mathcal M)^k_{b\Omega}$ on $k$-forms for the complex Laplacian $\Box$ on…

This note discusses the problem of the effective termination of Kohn's algorithm for subelliptic multipliers for bounded smooth weakly pseudoconvex domains of finite type. We give a complete proof for the case of special domains of finite…

Let $M$ be a relatively compact $C^2$ domain in a complex manifold $\mathcal M$ of dimension $n$. Assume that $H^{1}(M,\Theta)=0$ where $\Theta$ is the sheaf of germs of holomorphic tangent fields of $M$. Suppose that the Levi-form of the…

We provide a solution to the effectiveness problem in Kohn's algorithm for generating holomorphic subelliptic multipliers for $(0,q)$ forms for arbitrary $q$. As an application, we obtain subelliptic estimates for $(0,q)$ forms with…

We study the $\bar{\partial}_b$-Neumann problem for domains $\Omega$ contained in a strictly pseudoconvex manifold M^{2n+1} whose boundaries are noncharacteristic and have defining functions depending solely on the real and imaginary parts…

We show that every bordered Riemann surface, $M$, with smooth boundary $bM$ admits a proper holomorphic map $M\to \Omega$ into any bounded strongly pseudoconvex domain $\Omega$ in $\mathbb C^n$, $n>1$, extending to a smooth map $f:\overline…

We prove non-subelliptic estimates for the tangential Cauchy-Riemann system over a weakly "$q$-pseudoconvex" higher codimensional submanifold $M$ of $\C^n$. Let us point out that our hypotheses do not suffice to guarantee subelliptic…

The d-bar-Neumann operator on (0,q)-forms ($1\le q \le n$) on a bounded convex domain Omega in C^n is compact if and only if the boundary of Omega contains no complex analytic (equivalently: affine) variety of dimension greater than or…

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…

In 1995, Dan Guan constructed examples of non-Kahler, simply-connected holomorphically symplectic manifolds. An alternative construction, using the Hilbert scheme of Kodaira-Thurston surface, was given by F. Bogomolov. We investigate…

Consider a smooth manifold with a smooth metric which changes bilinear type from Riemann to Lorentz on a hypersurface $\Sigma$ with radical tangent to $\Sigma$. Two natural bilinear symmetric forms appear there, and we use it to analyze the…