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Title: Homogeneous variational problems: a minicourse (English)
Author: Saunders, David J.
Language: English
Journal: Communications in Mathematics
ISSN: 1804-1388
Volume: 19
Issue: 2
Year: 2011
Pages: 91-128
Summary lang: English
Category: math
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. (English)
Keyword: calculus of variations
Keyword: parametric problems
MSC: 35A15
MSC: 58A10
MSC: 58A20
idZBL: Zbl 1257.58012
idMR: MR2897264
Date available: 2012-04-06T06:17:09Z
Last updated: 2013-10-22
Stable URL:
Reference: [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 Zbl 1224.58012, MR 2545653, 10.1007/s10587-009-0044-0
Reference: [2] Giaquinta, M., Hildebrandt, S.: Calculus of Variations II. Springer 1996 MR 1385926
Reference: [3] Kolář, I., Michor, P.W., Slovák, J.: Natural Operations in Differential Geometry. Springer 1993 MR 1202431
Reference: [4] Rund, H.: The Hamilton-Jacobi Equation in the Calculus of Variations. Krieger 1973
Reference: [5] Saunders, D.J.: Homogeneous variational complexes and bicomplexes. J. Geom. Phys. 59 2009 727-739 Zbl 1168.58006, MR 2510165
Reference: [6] Saunders, D.J.: Some geometric aspects of the calculus of variations in several independent variables. Comm. Math. 18 (1) 2010 3-19 Zbl 1235.58014, MR 2848502


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