Finite energy surfaces and the chord problem (Q1974885)

The paper is a study of a conjecture by \textit{V. I. Arnol'd} [Russ. Math. Surv. 41, No. 6, 1-21 (1986; Zbl 0649.58010)] relative to a special class of orbits of the Reeb vector field associated to a contact form. These orbits are called characteristic chords and, as for many important results in symplectic topology, the main tool is \textit{M. Gromov's} theory of pseudoholomorphic curves [Invent. Math. 82, 307-347 (1985; Zbl 0592.53025)], more precisely pseudoholomorphic half-planes of finite energy.