We measured the static and dynamic dielectric properties of phosphatidylcholine (PC) spherical membranes (liposomes) over a wide range of temperature and for different liposome radii, pH, and liposomes concentration. Within the investigated temperature range, the physical state of the membrane goes from a gellike to a fluidlike phase, passing through a narrow (approximate to 10 degreesC) intermediate state, the Ripple phase, characterized by permanent surface undulations of defined wavelength and amplitude. The dielectric properties of the ripple phase are anomalous, the mean static permittivity is higher than that of the gel and fluid phases (where no undulations are present), while the average relaxation frequencies is smaller. Furthermore, the static dielectric permittivity of the fluid phase is much higher than that of the gel phase, while the relaxation frequencies behave just in the opposite way. In order to rationalize this complex behavior we have developed a dynamic mean-field model aimed to calculate the electric polarization and the dipolar relaxation for an array of strongly interacting dipoles anchored to the membrane surface and rotating over either a planar (gel and fluid phases) or a corrugated surface (the ripple phase). The dipoles mimic the highly polar (approximate to 20 Debyes) head groups of PC molecules. The model correctly predicts, albeit qualitatively, most of the observed dielectric anomalies essentially related to the changes of the dipole-dipole correlation induced by the membrane surface undulations.