Lemma 3.2 . [04TZ]

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Lemma 3.2.

Fix $x\in\Sigma_{v}$ . For a supporting slope $p$ at $x$ , let

d_{1}(h)\geq d_{2}(h)\geq...\geq d_{n}(h)

denote the axis lengths of the John ellipsoid of the section $S_{h,p}^{v}(x)$ . Then

\frac{d_{n-1}(h)}{h^{1/2}}\rightarrow 0\text{ as }h\rightarrow 0.