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Homogeneous variational problems: a minicourse

David J. Saunders — 2011

Communications in Mathematics

A Finsler geometry may be understood as a homogeneous variational problem, where the Finsler function is the Lagrangian. The extremals in Finsler geometry are curves, but in more general variational problems we might consider extremal submanifolds of dimension m . In this minicourse we discuss these problems from a geometric point of view.

Jets and the variational calculus

David J. Saunders — 2021

Communications in Mathematics

We review the approach to the calculus of variations using Ehresmann's theory of jets. We describe different types of jet manifold, different types of variational problem and different cohomological structures associated with such problems.

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