Almgren’s three-legged starfish
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.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Geometric and Algebraic Topology
Analytic and geometric function theory
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Publication date
- 4 September 2026
- Language
- EN