PreprintCC BY-NC-ND 4.0arXiv
Optimal Slicing Problems
Abstract
Given a bounded open set V⊂ ℝ2, 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 ∂ V.
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BibTeX
@misc{bressan2026optimal,
title = {{Optimal Slicing Problems}},
author = {Alberto Bressan and Maria Teresa Chiri and Elsa M. Marchini},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36149},
eprint = {2609.36149},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36149},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Optimal Slicing Problems
AU - Alberto Bressan
AU - Maria Teresa Chiri
AU - Elsa M. Marchini
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.36149
UR - https://arxiv.org/abs/2609.36149
AB - Given a bounded open set V⊂ 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 ∂ V.
ER -