M. Stephen

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20152018

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math.MG2018

Applications of Grünbaum-type inequalities

Matthew Stephen, Vladyslav Yaskin

Let $1 \leq i \leq k < n$ be integers. We prove the following exact inequalities for any convex body $K \subset R^{n}$ with centroid at the origin, and any $k$ -dimensional subs…

math.MG2018

Maximal perimeters of polytope sections and origin-symmetry

Matthew Stephen

Let $P \subset R^{n}$ $(n \geq 3)$ be a convex polytope containing the origin in its interior. Let $\mbox{vol}_{n-2} \big( \mbox{relbd} ( P\cap\lbrace tξ+ ξ^\perp \rbrace ) \bi…