The minimum length of an axis-aligned rectangular tiling of a flat torus

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Hau-Yi Lin, Wu-Hsiung Lin, Gerard J. Chang
DOI: 10.48550/arxiv.2603.04765
Cited by: 0

Abstract

A flat torus is the quotient of the Euclidean plane over a lattice generated by a basis, and an axis-aligned rectangular tiling of a flat torus is a partition into finitely many rectangles whose sides are axis-aligned. We provide the minimum sum of the perimeter of rectangles for an axis-aligned rectangular tiling, and prove that it is attainable by either exactly one rectangle or exactly two rectangles.

Fields of Study & Subjects

Mathematics and Applications Computational Geometry and Mesh Generation Geometric Analysis and Curvature Flows

Publication details

Journal / source
arXiv (Cornell University)
Publication date
5 March 2026
Language
EN
Document type
Preprint