In the second lecture, we introduce a space of measures that represent submanifolds, and we obtain a set of stability conditions that are strictly more general than the Euler-Lagrange equations. To show this, we give three examples that, respectively, recover those equations, produce higher-dimensional analogues of energy conservation, and give a very general version of the weak KAM theorem.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/5527