| 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:
|
http://hdl.handle.net/10338.dmlcz/142095 |
| . |
| 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 |
| . |
