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The notion of dynamically convex has been studied since it was introduced byHofer, Wysocki and Zehnder. In particular, they showed that there muse exist aglobal surface of section of disk type binding a periodic orbit for the Reebvector field in dynamically convex $(S^{3},\lambda)$ by using pseudoholomorphiccurves. Recently Hryniewicz and Salom\~ao showed the same result for $L(2,1)$by developing the original technique and after that Schneider generalized it to$(L(p,1),\xi_{\mathrm{std}})$. The main purpose of this paper is to introducean alternative approach of using Embedded contact homology. In particular, wefind a global surface of section of disk type in dynamically convex$(L(p,p-1),\xi_{\mathrm{std}})$ and relate their periods to the first ECHspectrum.

Dynamically convex and global surface of section in $L(p,p-1)$ from the viewpoint of ECH