On The Image Of The Hilbert Map

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arxiv 2208.13407 v2 pith:YAU3TJ7J submitted 2022-08-29 math.DG

Jingzhou Sun This is my paper · ORCID

classification math.DG

keywords hilbertimageconditionnecessarysufficientsurjectivetalk

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We talk about the image of the Hilbert map. We show the necessary and sufficient condition that the Hilbert map is surjective.

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Quantitative injectivity of the Fubini--Study map
math.AG 2025-02 conditional novelty 6.0 of 10

The Fubini-Study map is quantitatively injective: the Hilbert-Schmidt distance between two metrics is bounded by k^n times the W^{2,2} norm of the associated function.