Four closed characteristics on compact star-shaped hypersurfaces in ℝ⁸

2024/09/02 by Huagui Duan, Dong Xie, Duan, Huagui +1
Mathematics · #34C25 #37J46 #58E05 #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2409.04460

openalex publication_date 2024/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we proved that for every non-degenerate C³ compact star-shaped hypersurface Σ in ℝ⁸ which carries no prime closed characteristic of Maslov-type index -1, there exist at least four prime closed characteristics on Σ.

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