2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/221688We study metric and analytic properties of generalized lemniscates E_t(f)={z:ln|f(z)|=t}, where f is an analytic function. Our main result states that the length function |E_t(f)| is a bilateral Laplace transform of a certain positive measure. In particular, the function ln|E_t(f)| is convex on any interval free of critical points of ln|f|. As another application we deduce explicit formulas of the length function in some special cases.18 pagesComplex VariablesDifferential Geometry30E05; 42A82; 44A10text