Direct products for the Hamiltonian density property

Andrist, Rafael Benedikt (author), Huang, Gaofeng (author)

We show that the direct product of two Stein manifolds with the Hamiltonian density property enjoys the Hamiltonian density property as well. We investigate the relation between the Hamiltonian density property and the symplectic density property. We then establish the Hamiltonian and the symplectic density property for $({\mathbb C}^{\ast})^{2n}$ and for the so-called traceless Calogero-Moser spaces. As an application we obtain a Carleman-type approximation for Hamiltonian diffeomorphisms of a real form of the traceless Calogero-Moser space.

• Language: English
• Keywords: Hamiltonian density property, symplectic density property, direct product, traceless Calogero-Moser space, holomorphic symplectic automorphism
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2026
• Number of pages: 23 str.
• Numbering: Vol. 36, iss. 1, art. 8
• PID: 20.500.12556/RUL-179002
• UDC: 517.5
• ISSN on article: 1050-6926
• DOI: 10.1007/s12220-025-02246-3
• COBISS.SI-ID: 257833731
• Publication date in RUL: 03.02.2026

Record is a part of a journal

• Title: The Journal of geometric analysis
• Shortened title: J. geom. anal.
• Publisher: Springer, Mathematica Josephina
• ISSN: 1050-6926
• COBISS.SI-ID: 30685696

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Projects

• Funder: EC - European Commission
• Funding programme: HE
• Project number: 101053085
• Name: Holomorphic Partial Differential Relations
• Acronym: HPDR

• Funder: SNSF - Swiss National Science Foundation
• Project number: 200021-207335