Morse theory for elastica

P. Schrader

    Research output: Contribution to journalArticlepeer-review

    4 Citations (Scopus)


    ©American Institute of Mathematical Sciences.In Riemannian manifolds the elastica are critical points of the restriction of total squared geodesic curvature to curves with fixed length which satisfy first order boundary conditions. We verify that the Palais-Smale condition holds for this variational problem, and also the related problems where the admissible curves are required to satisfy zeroth order boundary conditions, or first order periodicity conditions. We also prove a Morse index theorem for elastica and use the Morse inequalities to give lower bounds for the number of elastica of each index in terms of the Betti numbers of the path space.
    Original languageEnglish
    Pages (from-to)235-256
    Number of pages22
    JournalJournal of Geometric Mechanics
    Issue number2
    Publication statusPublished - Jun 2016


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