On the embedding of 1-convex manifolds with 1-dimensional exceptional set

Lucia Alessandrini; Giovanni Bassanelli

Displaying similar documents to “On the embedding of 1-convex manifolds with 1-dimensional exceptional set”

Partial integrability on Thurston manifolds

Hyeseon Kim (2013)

Annales Polonici Mathematici

Similarity:

We determine the maximal number of independent holomorphic functions on the Thurston manifolds $M^{2 r + 2}$ , r ≥ 1, which are the first discovered compact non-Kähler almost Kähler manifolds. We follow the method which involves analyzing the torsion tensor dθ modθ, where $θ = (θ ¹, . . ., θ^{r + 1})$ are independent (1,0)-forms.

Non-Kähler compact complex manifolds associated to number fields

Karl Oeljeklaus, Matei Toma (2005)

Annales de l’institut Fourier

Similarity:

For algebraic number fields $K$ with $s > 0$ real and $2 t > 0$ complex embeddings and “admissible” subgroups $U$ of the multiplicative group of integer units of $K$ we construct and investigate certain $(s + t)$ -dimensional compact complex manifolds $X (K, U)$ . We show among other things that such manifolds are non-Kähler but admit locally conformally Kähler metrics when $t = 1$ . In particular we disprove a conjecture of I. Vaisman.

Erratum : “Closed transverse $(p, p)$ -forms on compact complex manifolds”

Lucia Alessandrini, Marco Andreatta (1987)

Compositio Mathematica

Similarity:

Generically strongly $q$ -convex complex manifolds

Terrence Napier, Mohan Ramachandran (2001)

Annales de l’institut Fourier

Similarity:

Suppose $ϕ$ is a real analytic plurisubharmonic exhaustion function on a connected noncompact complex manifold $X$ . The main result is that if the real analytic set of points at which $ϕ$ is not strongly $q$ -convex is of dimension at most $2 q + 1$ , then almost every sufficiently large sublevel of $ϕ$ is strongly $q$ -convex as a complex manifold. For $X$ of dimension $2$ , this is a special case of a theorem of Diederich and Ohsawa. A version for $ϕ$ real analytic with corners is also obtained.

The Bochner-Hartogs dichotomy for weakly 1-complete Kähler manifolds

Terence Napier, Mohan Ramachandran (1997)

Annales de l'institut Fourier

Similarity:

It is proved that if $M$ is a weakly 1-complete Kähler manifold with only one end, then $H_{c}^{1} (M, 𝒪) = 0$ or there exists a proper holomorphic mapping of $M$ onto a Riemann surface.

Analytic extension from non-pseudoconvex boundaries and $A (D)$ -convexity

Christine Laurent-Thiébaut, Egmon Porten (2003)

Annales de l’institut Fourier

Similarity:

Let $D \subset \subset ℂ^{n}, n \geq 2$ , be a domain with $C^{2}$ -boundary and $K \subset \partial D$ be a compact set such that $\partial D ∖ K$ is connected. We study univalent analytic extension of CR-functions from $\partial D ∖ K$ to parts of $D$ . Call $K$ CR-convex if its $A (D)$ -convex hull, $A (D) - hull (K)$ , satisfies $K = \partial D \cap A (D) - hull (K)$ ( $A (D)$ denoting the space of functions, which are holomorphic on $D$ and continuous up to $\partial D$ ). The main theorem of the paper gives analytic extension to $\partial D ∖ A (D) - hull (K)$ , if $K$ is CR- convex.

Displaying similar documents to “On the embedding of 1-convex manifolds with 1-dimensional exceptional set”

Partial integrability on Thurston manifolds

Non-Kähler compact complex manifolds associated to number fields

Erratum : “Closed transverse ( p , p ) -forms on compact complex manifolds”

Generically strongly q -convex complex manifolds

The Bochner-Hartogs dichotomy for weakly 1-complete Kähler manifolds

Analytic extension from non-pseudoconvex boundaries and A ( D ) -convexity

Erratum : “Closed transverse $(p, p)$ -forms on compact complex manifolds”

Generically strongly $q$ -convex complex manifolds

Analytic extension from non-pseudoconvex boundaries and $A (D)$ -convexity