An infinite dimensional balanced embedding problem I:existence

Jingzhou Sun; Song Sun

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arXiv · 2309.01097

An infinite dimensional balanced embedding problem I:existence

Jingzhou Sun·Song Sun

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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. 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 ODE; the convergence depends on a priori bounds that uses techniques in the proof of the Tauber-Hardy-Littlewood theorem.

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Jingzhou Sun, Song Sun. 2023-09-03. An infinite dimensional balanced embedding problem I:existence. https://arxiv.org/abs/2309.01097

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