Hyperplane conjecture for quotient spaces of $L_p$

Marius Junge

REVIEW

Hyperplane conjecture for quotient spaces of L_p

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv math/9312207 v1 pith:DYILINCB submitted 1993-12-22 math.FA

Hyperplane conjecture for quotient spaces of L_p

Marius Junge This is my paper

classification math.FA

keywords hyperplaneconjecturequotientspacesbanachcontainextendedfrac

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

0 comments

read the original 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.

Hyperplane conjecture for quotient spaces of L_p

discussion (0)