Oscar Garay

Universidad del Pais Vasco

Closed generalized elastic curves in space forms and applications
We consider variational problems associated to curvature energy functionals acting on spaces of curves. These actions generalize the Euler-Bernoulli elastic functional and other classical Lagrangians. We discuss a geometric method to integrate the Euler-Lagrange equations inreal space forms. The method is illustrated by giving some existence and classifications results of closed critical points for relevant examples. We also apply these results to several higher dimensional variational problems in submanifolds.