M. Dobbins

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20152021

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math.MG2019

The Inverse Kakeya Problem

Sergio Cabello, Otfried Cheong, Michael Gene Dobbins

We prove that the largest convex shape that can be placed inside a given convex shape $Q \subset R^{d}$ in any desired orientation is the largest inscribed ball of $Q$ . Th…

math.MG2018

Barycenters of points in polytope skeleta

Michael Gene Dobbins, Florian Frick

The first author showed that for a given point $p$ in an $nk$ -polytope $P$ there are $n$ points in the $k$ -faces of $P$ , whose barycenter is $p$ . We show that we can increase the d…

math.MG2017

Shadows of a Closed Curve

Michael Gene Dobbins, Heuna Kim, Luis Montejano +1

A shadow of a geometric object $A$ in a given direction $v$ is the orthogonal projection of $A$ on the hyperplane orthogonal to $v$ . We show that any topological embedding of a cir…