Digitalni repozitorij raziskovalnih organizacij Slovenije

Iskanje po repozitoriju
A+ | A- | Pomoč | SLO | ENG

Iskalni niz: išči po
išči po
išči po
išči po

Možnosti:
  Ponastavi


Iskalni niz: "ključne besede" (density property) .

1 - 3 / 3
Na začetekNa prejšnjo stran1Na naslednjo stranNa konec
1.
Recent developments on Oka manifolds
Franc Forstnerič, 2023, pregledni znanstveni članek

Povzetek: In this paper we present the main developments in Oka theory since the publication of my book "Stein Manifolds and Holomorphic Mappings (The Homotopy Principle in Complex Analysis)", 2nd ed., Springer, 2017. We also give several new results, examples and constructions of Oka domains in Euclidean and projective spaces. Furthermore, we show that for $n > 1$ the fibre $\mathbb C^n$ in a Stein family can degenerate to a non-Oka fibre, thereby answering a question of Takeo Ohsawa. Several open problems are discussed.
Ključne besede: Oka manifold, Oka map, Stein manifold, elliptic manifold, algebraically subelliptic manifold, Calabi–Yau manifold, density property
Objavljeno v DiRROS: 14.03.2024; Ogledov: 418; Prenosov: 454
.pdf Celotno besedilo (1014,41 KB)
Gradivo ima več datotek! Več...

2.
Oka domains in Euclidean spaces
Franc Forstnerič, Erlend Fornæss Wold, 2024, izvirni znanstveni članek

Povzetek: In this paper, we find surprisingly small Oka domains in Euclidean spaces $\mathbb C^n$ of dimension $n>1$ at the very limit of what is possible. Under a mild geometric assumption on a closed unbounded convex set $E$ in $\mathbb C^n$, we show that $\mathbb C^n\setminus E$ is an Oka domain. In particular, there are Oka domains only slightly bigger than a halfspace, the latter being neither Oka nor hyperbolic. This gives smooth families of real hypersurfaces $\Sigma_t \subset \mathbb C^n$ for $t \in \mathbb R$ dividing $\mathbb C^n$ in an unbounded hyperbolic domain and an Oka domain such that at $t=0$, $\Sigma_0$ is a hyperplane and the character of the two sides gets reversed. More generally, we show that if $E$ is a closed set in $\mathbb C^n$ for $n>1$ whose projective closure $\overline E \subset \mathbb{CP}^n$ avoids a hyperplane $\Lambda \subset \mathbb{CP}^n$ and is polynomially convex in $\mathbb{CP}^n\setminus \Lambda\cong\mathbb C^n$, then $\mathbb C^n\setminus E$ is an Oka domain.
Ključne besede: Oka manifold, hyperbolic manifolds, density property, projectively convex sets
Objavljeno v DiRROS: 19.02.2024; Ogledov: 219; Prenosov: 74
.pdf Celotno besedilo (278,96 KB)
Gradivo ima več datotek! Več...

3.
Complete nonsingular holomorphic foliations on Stein manifolds
Antonio Alarcón, Franc Forstnerič, 2024, izvirni znanstveni članek

Povzetek: Let $X$ be a Stein manifold of complex dimension $n \ge 1$ endowed with a Riemannian metric ${\mathfrak g}$. We show that for every integer $k$ with $\left[\frac{n}{2}\right] \le k \le n-1$ there is a nonsingular holomorphic foliation of dimension $k$ on $X$ all of whose leaves are topologically closed and ${\mathfrak g}$-complete. The same is true if $1\le k \left[\frac{n}{2}\right]$ provided that there is a complex vector bundle epimorphism $TX\to X \times \mathbb{C}^{n-k}$. We also show that if $\mathcal{F}$ is a proper holomorphic foliation on $\mathbb{C}^n$ $(n > 1)$ then for any Riemannian metric ${\mathfrak g}$ on $\mathbb{C}^n$ there is a holomorphic automorphism $\Phi$ of $\mathbb{C}^n$ such that the image foliation $\Phi_*\mathcal{F}$ is ${\mathfrak g}$-complete. The analogous result is obtained on every Stein manifold with Varolin's density property.
Ključne besede: Stein manifolds, complete holomorphic foliations, density property
Objavljeno v DiRROS: 19.02.2024; Ogledov: 186; Prenosov: 63
.pdf Celotno besedilo (433,06 KB)
Gradivo ima več datotek! Več...
Iskanje izvedeno v 0.12 sek.
Na vrh