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Keywords:
calculus of variations; parametric problems
calculus of variations; parametric problems
Summary:
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.
References:
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[5] Saunders, D.J.: Homogeneous variational complexes and bicomplexes. J. Geom. Phys. 59 2009 727-739 MR 2510165 | Zbl 1168.58006
[6] Saunders, D.J.: Some geometric aspects of the calculus of variations in several independent variables. Comm. Math. 18 (1) 2010 3-19 MR 2848502 | Zbl 1235.58014
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