Results 41 to 50 of about 799 (89)
On uniqueness of solutions to complex Monge–Ampère mean field equations
Bulletin of the London Mathematical Society, Volume 57, Issue 10, Page 3163-3180, October 2025.Abstract We establish the uniqueness of solutions to complex Monge–Ampère mean field equations when (minus) the temperature parameter is small. In the local setting of bounded hyperconvex domains, our result partially confirms a conjecture by Berman and Berndtsson. Our approach also extends to the global context of compact complex manifolds.
Chinh H. Lu, Trong‐Thuc Phung
wiley +1 more source
On Functions of Several Split‐Quaternionic Variables
Advances in Mathematical Physics, Volume 2016, Issue 1, 2016., 2016 Alesker studied a relation between the determinant of a quaternionic Hessian of a function and a specific complex volume form. In this note we show that similar relation holds for functions of several split‐quaternionic variables and point to some relations with geometry.
Gueo Grantcharov +2 more
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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 +2 more
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On Traces in Some Analytic Spaces in Bounded Strictly Pseudoconvex Domains
Journal of Function Spaces, Volume 2015, Issue 1, 2015., 2015 New sharp estimates of traces of Bergman type spaces of analytic functions in bounded strictly pseudoconvex domains are obtained. These are, as far as we know, the first results of this type which are valid for any bounded strictly pseudoconvex domains with smooth boundary.
Romi F. Shamoyan +2 more
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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
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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
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Holomorphically conjugate polynomial automorphisms of C2$\mathbb {C}^2$ are polynomially conjugate
Bulletin of the London Mathematical Society, Volume 56, Issue 12, Page 3745-3751, December 2024.Abstract We confirm a conjecture of Friedland and Milnor: if two polynomial automorphisms f$f$ and g∈Aut(AC2)$g\in \mathsf {Aut}(\mathbb {A}^2_\mathbf {C})$ with dynamical degree greater than 1 are conjugate by some holomorphic diffeomorphism φ:C2→C2$\varphi \colon \mathbf {C}^2\rightarrow \mathbf {C}^2$, then φ$\varphi$ is a polynomial automorphism ...
Serge Cantat, Romain Dujardin
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Geometric properties of domains related to $\mu$-synthesis
, 2014 In the paper we study the geometric properties of a large family of domains, called the generalized tetrablocks, related to the $\mu$-synthesis, containing both the family of the symmetrized polydiscs and the family of the $\mu_{1,n}$-quotients $\mathbb ...
Zapalowski, Pawel
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On the structure of Nevanlinna measures
Mathematische Nachrichten, Volume 297, Issue 7, Page 2488-2516, July 2024.Abstract In this paper, we study the structural properties of Nevanlinna measures, that is, Borel measures that arise in the integral representation of Herglotz–Nevanlinna functions. In particular, we give a characterization of these measures in terms of their Fourier transform, characterize measures supported on hyperplanes including extremal measures,
Mitja Nedic, Eero Saksman
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Stationary disks and Green functions in almost complex domains [PDF]
, 2011 Using generalized Riemann maps, normal forms for almost complex domains (D, J) with singular foliations by stationary disks are defined. Such normal forms are used to construct counterexamples and to determine intrinsic conditions, under which the ...
Patrizio, G., Spiro, A.
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