A survey on the Weinstein conjecture

Abstract

The Weinstein conjecture predicts that there is at least one periodic orbit for every compact contact hypersurface in a symplectic manifold, which turns out an important research direction in symplectic topology and contact topology. According to the methods of the research, this paper surveys the study on the Weinstein conjecture using the variational method and the pseudo-holomorphic curves method.

Keywords

Weinstein conjecture / periodic orbit / contact manifold / J-holomorphic curves / Reeb flow

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