Work

Morse index bound of simple closed geodesics on 2-spheres and strong Morse inequalities

Year: 2024

Type: article

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.

Source: Journal für die reine und angewandte Mathematik (Crelles Journal)

DOI: 10.1515/crelle-2024-0065

Author: Dongyeong Ko

Institution: Rutgers, The State University of New Jersey

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Award: Minimal Surfaces in Geometry and Topology