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arXiv · 2411.11462

The isominwidth problem on the 2-sphere

Ansgar Freyer·Ádám Sagmeister
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Abstract

Pál's isominwidth theorem states that for a fixed minimal width, the regular triangle has minimal area. A spherical version of this theorem was proven by Bezdek and Blekherman, if the minimal width is at most $\tfrac π2$. If the width is greater than $\tfrac π2$, the regular triangle no longer minimizes the area at fixed minimal width. We show that the minimizers are instead given by the polar sets of spherical Reuleaux triangles. Moreover, stability versions of the two spherical inequalities are obtained.

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Ansgar Freyer, Ádám Sagmeister. 2024-11-18. The isominwidth problem on the 2-sphere. https://arxiv.org/abs/2411.11462

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