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- W2113616621 abstract "We consider the isoperimetric inequality on the class of high-dimensional isotropic convex bodies. We establish quantitative connections between two well-known open problems related to this inequality, namely, the thin shell conjecture, and the conjecture by Kannan, Lovasz, and Simonovits, showing that the corresponding optimal bounds are equivalent up to logarithmic factors. In particular we prove that, up to logarithmic factors, the minimal possible ratio between surface area and volume is attained on ellipsoids. We also show that a positive answer to the thin shell conjecture would imply an optimal dependence on the dimension in a certain formulation of the Brunn-Minkowski inequality. Our results rely on the construction of a stochastic localization scheme for log-concave measures." @default.
- W2113616621 created "2016-06-24" @default.
- W2113616621 creator A5011758954 @default.
- W2113616621 date "2013-03-22" @default.
- W2113616621 modified "2023-10-10" @default.
- W2113616621 title "Thin Shell Implies Spectral Gap Up to Polylog via a Stochastic Localization Scheme" @default.
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- W2113616621 doi "https://doi.org/10.1007/s00039-013-0214-y" @default.
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