Journal of the
Korean Mathematical Society JKMS

Rabinowitz action functional is the Lagrange multiplier functional of the negative area functional to a constraint given by the mean value of a Hamiltonian. In this note we show that on a symplectization there is a one-to-one correspondence between gradient flow lines of Rabinowitz action functional and gradient flow lines of the restriction of the negative area functional to the constraint. In the appendix we explain the motivation behind this result. Namely that the restricted functional satisfies Chas-Sullivan additivity for concatenation of loops which the Rabinowitz action functional does in general not do.

Keywords: Lagrange multiplier, Kazdan Warner equation

MSC numbers: Primary 53D35, 57R58

Supported by: This work was partially supported by DFG grant FR 2637/2-2.