  Using general local conservations laws we derive dispersion relations for
edge modes in a slab of electron liquid confined by a symmetric potential. The
dispersion relations are exact up to $\lambda^{2} q^{2}$, where $q$ is a wave
vector and $\lambda$ is an effective screening length. For a harmonic external
potential the dispersion relations are expressed in terms of the {\em exact}
static pressure and dynamic shear modulus of a homogeneous liquid with the
density taken at the slab core. We also derive a simple expression for the
frequency shift of the dipole (Kohn) modes in nearly parabolic quantum dots in
a magnetic field.
