arXiv Open Access 2025

Almgren's Three-Legged Starfish

Christos Mantoulidis Jared Marx-Kuo

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Abstrak

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.

Topik & Kata Kunci

math.DG

Penulis (2)

Christos Mantoulidis

Jared Marx-Kuo

Format Sitasi

APA MLA BibTeX

Mantoulidis, C., Marx-Kuo, J. (2025). Almgren's Three-Legged Starfish. https://arxiv.org/abs/2504.20895

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Informasi Jurnal

Tahun Terbit: 2025
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓