The length of a shortest closed geodesic and the area of a 2-dimensional sphere

Rotman, R.

doi:10.1090/S0002-9939-06-08297-9

The length of a shortest closed geodesic and the area of a $2$-dimensional sphere
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Proc. Amer. Math. Soc. 134 (2006), 3041-3047 Request permission

Abstract:

Let $M$ be a Riemannian manifold homeomorphic to $S^2$. The purpose of this paper is to establish the new inequality for the length of a shortest closed geodesic, $l(M)$, in terms of the area $A$ of $M$. This result improves previously known inequalities by C.B. Croke (1988), by A. Nabutovsky and the author (2002) and by S. Sabourau (2004).

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