Almgren's Three-Legged Starfish

Christos Mantoulidis; Jared Marx-Kuo

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arXiv · 2504.20895

Almgren's Three-Legged Starfish

Christos Mantoulidis·Jared Marx-Kuo

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Abstract

In this note we use classical tools from min-max and hyperbolic geometry to substantiate a folklore example in Almgren--Pitts min-max theory, the three-legged starfish metric on a 2-sphere, whose systolic length, Almgren--Pitts width, and Gromov--Guth width are attained by ``figure-eight'' geodesics. We also recover a hyperbolic geometry fact about ``figure-eight'' geodesics using min-max.

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Christos Mantoulidis, Jared Marx-Kuo. 2025-04-29. Almgren's Three-Legged Starfish. https://arxiv.org/abs/2504.20895

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