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On the existence of three closed not self-intersecting geodesics on manifolds homeomorphic to a two-dimensional sphere. (Russian) Zbl 0771.53027
The author constructs a local combinatorial length-decreasing deformation for curves on a surface and gives a complete proof of the Lusternik-Schnirelman three geodesics theorem. The steps of the proof use Besicovitch’s covering lemma and are similar to J. Jost [Arch. Math. 53, No. 5, 497–509 (1989; Zbl 0676.58018)] with certain amendments of the text.

MSC:
53C22 Geodesics in global differential geometry
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