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Natural isoperimetric conditions in the calculus of variations

1935; Duke University Press; Volume: 1; Issue: 2 Linguagem: Inglês

10.1215/s0012-7094-35-00118-1

1547-7398

George D. Birkhoff, Magnus R. Hestenes,

Elasticity and Wave Propagation

The theorem of Birkhoff (Dynamical Systems, p. 135) that any surface homeomorphic with a hypersphere has at least one closed geodesic depends for its proof upon a simple case of this extension.4 It is understood that every sub-k-cycle of a k-cycle in 91k is also in 9k, and that homologous k-cycle in 9k having the same critical k-sets are to be regarded as identical.A similar remark holds for k-chains in S2k.