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Hyperplane conjecture for quotient spaces of $L_p$

Marius Junge
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Abstract

We give a positive solution for the hyperplane conjecture of quotient spaces F of $L_p$, where $1<p\kll\infty$. \[ vol(B_F)^{\frac{n-1}{n}} \kl c_0 \pl p' \pl \sup_{H \p hyperplane} vol(B_F\cap H) \pl.\] This result is extended to Banach lattices which does not contain $\ell_1^n$'s uniformly. Our main tools are tensor products and minimal volume ratio with respect to $L_p$-sections.

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Marius Junge. 1993-12-22. Hyperplane conjecture for quotient spaces of $L_p$. https://arxiv.org/abs/math/9312207

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