Journal of the
Korean Mathematical Society

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008



J. Korean Math. Soc. 2023; 60(2): 375-393

Online first article February 17, 2023      Printed March 1, 2023

Copyright © The Korean Mathematical Society.

The gradient flow equation of Rabinowitz action functional in a symplectization

Urs Frauenfelder

Augsburg University


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.

Stats or Metrics

Share this article on :

Related articles in JKMS