Results 41 to 50 of about 122 (116)

On a higher dimensional worm domain and its geometric properties

Journal of the London Mathematical Society, Volume 111, Issue 6, June 2025.
Abstract We construct new three‐dimensional variants of the classical Diederich–Fornæss worm domain. We show that they are smoothly bounded, pseudoconvex, and have nontrivial Nebenhülle. We also show that their Bergman projections do not preserve the Sobolev space for sufficiently large Sobolev indices.
Steven G. Krantz, Marco M. Peloso, Caterina Stoppato   +2 more
wiley   +1 more source

Uniformization of strictly pseudoconvex domains. II [PDF]

Izvestiya: Mathematics, 2005
It is shown that two strictly pseudoconvex Stein domains with real analytic boundaries have biholomorphic universal coverings provided that their boundaries are locally biholomorphically equivalent. This statement can be regarded as a higher dimensional analogue of the Riemann uniformization theorem.
Nemirovski, Stefan, Shafikov, Rasul
openaire   +2 more sources

CR$CR$ analysis via local uniform completion, a sharp maximum modulus principle and holomorphic extension

Journal of the London Mathematical Society, Volume 111, Issue 5, May 2025.
Abstract Using iterated uniform local completion, we introduce a notion of continuous CR$CR$ functions on locally closed subsets of reduced complex spaces, generalising both holomorphic functions and CR$CR$ functions on CR$CR$ submanifolds. Under additional assumptions of set‐theoretical weak pseudo‐concavity, we prove optimal maximum modulus ...
Mauro Nacinovich, Egmont Porten
wiley   +1 more source

An exotic calculus of Berezin–Toeplitz operators

Mathematika, Volume 71, Issue 2, April 2025.
Abstract We develop a calculus of Berezin–Toeplitz operators quantizing exotic classes of smooth functions on compact Kähler manifolds and acting on holomorphic sections of powers of positive line bundles. These functions (classical observables) are exotic in the sense that their derivatives are allowed to grow in ways controlled by local geometry and ...
Izak Oltman
wiley   +1 more source

On the compactification of strongly pseudoconvex surfaces [PDF]

Proceedings of the American Mathematical Society, 1981
In this paper, we shall prove that the compactification of a strongly pseudoconvex surface is either a projective algebraic or an Inoue surface. Furthermore, we shall construct an example of a strongly pseudoconvex surface X
openaire   +4 more sources

Non‐cyclicity and polynomials in Dirichlet‐type spaces of the unit ball

Bulletin of the London Mathematical Society, Volume 56, Issue 12, Page 3905-3919, December 2024.
Abstract We give a description of the intersection of the zero set with the unit sphere of a polynomial that is zero‐free in the unit ball of Cn${\mathbb {C}}^n$. This description leads to a necessary condition for a polynomial to be cyclic in Dirichlet‐type spaces of the unit ball.
Dimitrios Vavitsas, Konstantinos Zarvalis   +1 more
wiley   +1 more source

On Locally Uniformly $A$-Pseudoconvex Algebras

Rocky Mountain Journal of Mathematics, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Abel, M., Kinani, A. El, Oudadess, M.
openaire   +2 more sources

New estimates of Rychkov's universal extension operator for Lipschitz domains and some applications

Mathematische Nachrichten, Volume 297, Issue 4, Page 1407-1443, April 2024.
Abstract Given a bounded Lipschitz domain Ω⊂Rn$\Omega \subset \mathbb {R}^n$, Rychkov showed that there is a linear extension operator E$\mathcal {E}$ for Ω$\Omega$, which is bounded in Besov and Triebel‐Lizorkin spaces. In this paper, we introduce some new estimates for the extension operator E$\mathcal {E}$ and give some applications.
Ziming Shi, Liding Yao
wiley   +1 more source

Analyticity in the boundary of a pseudoconvex domain [PDF]

Proceedings of the American Mathematical Society, 1985
Let D D be a bounded pseudoconvex domain with
openaire   +1 more source

Closed 3‐forms in five dimensions and embedding problems

Journal of the London Mathematical Society, Volume 109, Issue 4, April 2024.
Abstract We consider the question if a five‐dimensional manifold can be embedded into a Calabi–Yau manifold of complex dimension 3 such that the real part of the holomorphic volume form induces a given closed 3‐form on the 5‐manifold. We define an open set of 3‐forms in dimension five which we call strongly pseudoconvex, and show that for closed ...
Simon Donaldson, Fabian Lehmann
wiley   +1 more source