Stefan Steinerberger

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20242026

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math.MG2026

A Remark on the Odd Area of Unit Disks

Stefan Steinerberger

Let $F$ be a family of $n$ unit disks in $R^{2}$ with $n$ being odd. We use $\mbox{OA}(F)$ to denote the area of the set of points that is covered by an odd number of disks.…

math.MG2026

Distance Equilibrium Measures and Curvature in Metric Spaces

Stefan Steinerberger

Let $(X, d)$ be a compact metric space. We consider the behavior of probability measures $I^¼$ with the property that $$ \int_{X} d(x, y) dÎ¼(y) \qquad \mbox{is independent of}~x \in…

math.MG2025

A Stability Version of the Jones Opaque Set Inequality

Stefan Steinerberger

Let $I^c ◯ \subset R^{2}$ be a bounded, convex set. A set $O \subset R^{2}$ is an opaque set (for $I^c ◯$ ) if every line that intersects $I^c ◯$ also intersects $O$ . What is th…