摘要:In this paper, we study the Hofer-Zehnder capacity and the Weinstein conjecture in symplectic manifold (M×R2n, ω(?)σ). Let us define l1(M, ω)=inf{ω, α|0, α∈π2(M)}. Suppose l1(M, ω)O, Oπr22/1 l1(M, ω). Then CHZ(M×B(r))=CHZ(M×Z(r))=πr2. In the case M is a point {P}, we obtain the well-known result at present. For n1, consider on Cpn-1 the standard symplectic form co such that ω[u]=n for a generator u of H2(CPn-1. Suppose Oπr22/1 n. ThenCHZ(M×B(r))=CHZ(M×Z(r))=πr2.As an application, we claim that the Weinstein conjecture in M×Z(r) is proved correct.