Previous |  Up |  Next


calculus of variations; parametric problems
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.
[1] Crampin, M., Saunders, D.J.: Some concepts of regularity for parametric multiple-integral problems in the calculus of variations. Czech Math. J. 59 (3) 2009 741-758 DOI 10.1007/s10587-009-0044-0 | MR 2545653 | Zbl 1224.58012
[2] Giaquinta, M., Hildebrandt, S.: Calculus of Variations II. Springer 1996 MR 1385926
[3] Kolář, I., Michor, P.W., Slovák, J.: Natural Operations in Differential Geometry. Springer 1993 MR 1202431
[4] Rund, H.: The Hamilton-Jacobi Equation in the Calculus of Variations. Krieger 1973
[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
Partner of
EuDML logo