The determinant of the Dirichlet-to-Neumann map for a surface with boundary and periods of holomorphic differentials on its double
The paper connects length spectra of a surface M and its double 2M to periods of holomorphic differentials on 2M. It derives formula (7), which relates the determinant of the Dirichlet-to-Neumann map to these periods, establishing a link between spectral data and geometric invariants.