Volume of intersections and sections of the unit ball of ℓⁿ_{𝑝}

Schmuckenschläger, Michael

doi:10.1090/S0002-9939-98-04179-3

Volume of intersections and sections of the unit ball of $\ell ^n_p$
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by Michael Schmuckenschläger

Proc. Amer. Math. Soc. 126 (1998), 1527-1530

DOI: https://doi.org/10.1090/S0002-9939-98-04179-3

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Abstract:

An asymptotic formula for the volume of the intersection of a suitable multiple of the unit ball of $\ell _p^n$ and the cube $[-1/2,1/2]^n$ will be proved. We also show that the isotropic constant of the unit ball of $\ell _n^p, 1\le p\le 2$, is bounded by $1/\sqrt {12}$.

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