PreprintarXiv licencearXiv
On convex spiral equicoverings of masses
Abstract
Convex spiral equicoverings were recently introduced by Espinosa-García, Martínez-Sandoval and Roldán-Pensado. They left open the question of whether every planar mass admits a convex (3k,k+1)-spiral equicovering. In this paper we give an affirmative answer to this question. To be precise, we prove the following: Given an integer k ≥ 2, for every planar mass there is a fan consisting of 3k equal-mass sectors such that the union of every k+1 consecutive sectors is convex.
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BibTeX
@misc{roldanpensado2026convex,
title = {{On convex spiral equicoverings of masses}},
author = {Edgardo Roldán-Pensado},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23746},
eprint = {2609.23746},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23746},
}
RIS
TY - UNPB
TI - On convex spiral equicoverings of masses
AU - Edgardo Roldán-Pensado
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2609.23746
UR - https://arxiv.org/abs/2609.23746
AB - Convex spiral equicoverings were recently introduced by Espinosa-García, Martínez-Sandoval and Roldán-Pensado. They left open the question of whether every planar mass admits a convex (3k,k+1)-spiral equicovering. In this paper we give an affirmative answer to this question. To be precise, we prove the following: Given an integer k ≥ 2, for every planar mass there is a fan consisting of 3k equal-mass sectors such that the union of every k+1 consecutive sectors is convex.
ER -