Morse Index bound of simple closed geodesics on 2-spheres and strong Morse Inequalities

2023/03/01 by Dongyeong Ko, Ko, Dongyeong · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #Bone Metabolism and Diseases #Bone health and osteoporosis research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2303.00644

openalex publication_date 2023/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a Morse-theoretic characterization of simple closed geodesics on Riemannian 2-spheres. On any Riemannian 2-sphere endowed with a generic metric, we show there exists a simple closed geodesic with Morse index 1, 2 and 3. In particular, for an orientable Riemannian surface we prove strong Morse inequalities for the length functional applied to the space of simple closed curves.

Cited by

• Min-max theory and minimal surfaces with prescribed genus

Related

• Geodesic laminations with closed ends on surfaces and Morse index; Kupka-Smale metrics
• Metrics without Morse index bounds
• Index, Intersections, and Multiplicity of Min-Max Geodesics
• Two short closed geodesics on a sphere of odd dimension
• Morse Index Bound for Minimal Two Spheres