4 problems

Let $\mathcal{D}$ be the set of circle local homeomorphisms $f:\mathbb{S}^1\to\mathbb{S}^1$ that are topologically conjugate to the doubling map. For $f\in\mathcal{D}$, let $p$ be…

Let $n$ be a positive integer, and consider the $n\times n$ grid. Suppose it is covered by $m$ circles, with no two circles having equal radius. Distinct-radii circle-covering conj…

A totally separable packing of convex bodies is one in which every pair can be separated by a hyperplane that intersects the interior of none of the bodies. Consider the extreme de…

A covering of the plane by unit circles has margin $\mu\in[0,1]$ if removing any one circle creates empty space that can be covered by a circle of radius $1-\mu$. Bezdek–Kuperberg…