Symplectic capacity and the Weinstein conjecture in certain cotangent bundles and Stein manifolds (Q1895858)

Let \((M,\omega)\) be a compact symplectic manifold with contact type boundary and \((D,\sigma)\) be a a two-dimensional disk whose area \(\int_D\sigma> 0\) is strictly less than \(\inf\{\int_{S^2} u^*\omega\mid u\in \pi_2(M)\), \(\int_{S^2} u^*\omega>0\}\). The author proves that, under these assumptions, the Hofer-Zehnder capacity of \((M\times D,\omega\oplus\sigma)\) satisfies \(c(M\times D,\omega\oplus \sigma)<\int_D\sigma\). Finding an upper bound for the capacity of a symplectic manifold implies the Weinstein conjecture; here this means that any compact hypersurface in \((M\times D,\omega\oplus \sigma)\) of contact type carries a closed characteristic.