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arXiv · 2609.36149

Optimal Slicing Problems

Alberto Bressan·Maria Teresa Chiri·Elsa M. Marchini
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Abstract

Given a bounded open set $V\subset \mathbb{R}^2$, we consider the problem of slicing this set by a family of curves, whose average length is as small as possible. The first sections of the paper prove the existence of an optimal slicing and establish a connection with the problem of eradicating an invasive biological species from an island, considered in \cite{BMS}. Namely, an optimal slicing can be obtained as a limit of minimum time eradication strategies. The second part of the paper derives various necessary conditions for optimality, describing the behavior of an optimal slicing strategy in the interior of $V$ and near the boundary $\partial V$.

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Alberto Bressan, Maria Teresa Chiri, Elsa M. Marchini. 2026-09-28. Optimal Slicing Problems. https://arxiv.org/abs/2609.36149

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