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arXiv · 2609.23746

On convex spiral equicoverings of masses

Edgardo Roldán-Pensado
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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 $k \ge 2$, 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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Edgardo Roldán-Pensado. 2026-09-20. On convex spiral equicoverings of masses. https://arxiv.org/abs/2609.23746

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