M. Stephen

activity

20152018

collaborators

4 papers

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…

math.MG2017

Grünbaum's inequality for sections

Sergii Myroshnychenko, Matthew Stephen, Ning Zhang

We show \begin{align*} \frac{ \int_{E \cap θ^+} f(x) dx }{ \int_E f(x) dx } \geq \left(\frac{k γ+1}{(n+1) γ+1}\right)^{\frac{k γ+1}γ} \end{align*} for all $k$ -dimensional subspaces…

math.MG2015

Stability results for sections of convex bodies

Matthew Stephen, Vladyslav Yaskin

It is shown by Makai, Martini, and Ódor that a convex body $K \subset R^{n}$ , all of whose maximal sections pass through the origin, must be origin-symmetric. We prove a stabi…