A survey on Weinstein conjecture. (Chinese. English summary) Zbl 1413.53126
Summary: Weinstein’s conjecture predicts that every compact contact hypersurface in the symplectic manifold has at least one periodic orbit, and it is an important direction of research in symplectic topology and contact topology. According to the methods of the research, this note surveys the study on Weinstein conjecture using variational methods and pseudo-holomorphic curves methods.