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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).

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