An Infinite Dimensional Balanced Embedding Problem I: Existence
Abstract
Abstract We investigate the problem of balanced embedding of a non-compact complex manifold into an infinite-dimensional projective space. In this paper, we prove the existence of such an embedding in a model case of a complex space. The strategy is by using a gradient flow in a Hilbert space; both the long-time existence and convergence at infinite time are non-trivial. The long time existence is established by choosing a perturbation of the ordinary differential equation; the convergence depends on a priori bounds that use techniques in the proof of the Tauber–Hardy–Littlewood theorem.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Quantum chaos and dynamical systems
Stability and Controllability of Differential Equations
Publication details
- Journal / source
- International Mathematics Research Notices
- Volume
- 2026
- Issue
- 8
- Publication date
- 1 April 2026
- Language
- EN