Results 51 to 60 of about 217,307 (157)

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

Wolfe Type Second Order Nondifferentiable Symmetric Duality in Multiobjective Programming over Cone with Generalized (K, F)‐Convexity

International Scholarly Research Notices, Volume 2014, Issue 1, 2014., 2014
A new class of second order (K, F) pseudoconvex function is introduced with example. A pair of Wolfe type second order nondifferentiable symmetric dual programs over arbitrary cones with square root term is formulated. The duality results are established under second order (K, F) pseudoconvexity assumption.
A. K. Tripathy, F. Ding, F. Zirilli
wiley   +1 more source

The Carath�odory distance in strongly pseudoconvex domains

Mathematische Annalen, 1994
Let \(G \Subset \mathbb{C}^ n\) be a strongly pseudoconvex domain and \(P_ 0\), \(Q_ 0 \in \partial G\). It is proved that there is a continuous double peak function \(f\) in \(G\) at \(P_ 0\), \(Q_ 0\), i.e., there exist a domain \(G' \Supset G\), two neighbourhoods \(U_ 1,U_ 2\) of \(P_ 0\) and \(Q_ 0\) respectively such that \(f:B_{U_ 1} \times B_ ...
openaire   +1 more source

Smooth equivalence of families of strongly pseudoconvex domains

, 2023
We establish a smoothness result for families of biholomorphisms between smooth families of strongly pseudoconvex domains, each with trivial biholomorphism group. This is accomplished by considering the Riemannian geometry of their Bergman metrics and proving a result about the smoothness of families of isometries between smooth families of Riemannian ...
Gaussier, Hervé, Gong, Xianghong, Zimmer, Andrew   +2 more
openaire   +2 more sources

The equation on variable strictly pseudoconvex domains

, 2017
We investigate regularity properties of the (partial derivative) over bar -equation on domains in a complex euclidean space that depend on a parameter. Both the interior regularity and the regularity in the parameter are obtained for a continuous family ...
Gong, Xianghong, Kim, Kang-Tae, Kang-Tae Kim, Xianghong Gong   +3 more
core   +1 more source

Dirac–Schrödinger operators, index theory and spectral flow

Journal of the London Mathematical Society, Volume 112, Issue 4, October 2025.
Abstract In this article, we study generalised Dirac–Schrödinger operators in arbitrary signatures (with or without gradings), providing a general KK$\textnormal {KK}$‐theoretic framework for the study of index pairings and spectral flow. We provide a general Callias Theorem, which shows that the index (or the spectral flow, or abstractly the K ...
Koen van den Dungen
wiley   +1 more source

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

Estimates of Invariant Metrics on Pseudoconvex Domains of Finite Type in C3

Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014
Let Ω be a smoothly bounded pseudoconvex domain in C3 and assume that z0 ∈ bΩ is a point of finite 1‐type in the sense of D’Angelo. Then, there are an admissible curve Γ ⊂ Ω ∪ {z0}, connecting points q0 ∈ Ω and z0 ∈ bΩ, and a quantity M(z, X), along z ∈ Γ, which bounds from above and below the Bergman, Caratheodory, and Kobayashi metrics in a small ...
Sanghyun Cho, Young Hwan You, Sung G. Kim   +2 more
wiley   +1 more source

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