The length of the shortest closed geodesic on positively curved 2-spheres

The length of the shortest closed geodesic on positively curved 2-spheres

We show that the shortest closed geodesic on a 2-sphere with non-negative curvature has length bounded above by three times the diameter. We prove a new isoperimetric inequality for 2-spheres with pinched curvature; this allows us to improve our bound on the length of the shortest closed geodesic in...

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Veröffentlicht in:Mathematische Zeitschrift 2022-03, Vol.300 (3), p.2519-2531
Hauptverfasser: Adelstein, Ian, Vargas Pallete, Franco
Format: Artikel
Sprache:eng
Schlagworte:
Curvature
Mathematics
Mathematics and Statistics
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Zusammenfassung:We show that the shortest closed geodesic on a 2-sphere with non-negative curvature has length bounded above by three times the diameter. We prove a new isoperimetric inequality for 2-spheres with pinched curvature; this allows us to improve our bound on the length of the shortest closed geodesic in the pinched curvature setting.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-021-02875-8