Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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THE GRADIENT FLOW EQUATION OF RABINOWITZ ACTION FUNCTIONAL IN A SYMPLECTIZATION

  • Received : 2022.03.17
  • Accepted : 2022.10.27
  • Published : 2023.03.01
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Abstract

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.

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Acknowledgement

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

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