Explicit metrics on S^d and weighted R^d for d≥4 violate Milman's spectral comparison conjectures, ruling out 1-Lipschitz transport maps; the abstract's extra dimension-2 and hemisphere results are not in the text.
Moment sequences of beta distribution.arXiv preprint arXiv:2112.13420,
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Spectral Obstructions to Contracting Transport Maps on Curved Spaces
Explicit metrics on S^d and weighted R^d for d≥4 violate Milman's spectral comparison conjectures, ruling out 1-Lipschitz transport maps; the abstract's extra dimension-2 and hemisphere results are not in the text.