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.
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Quantitative injectivity of the Fubini--Study map
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.