  Bending rigidity of a charged membrane or a charged polyelectrolyte screened
by monovalent counterions is known to be enhanced by electrostatic effects. We
show that in the case of screening by multivalent counterions the electrostatic
effects reduce the bending rigidity. This inversion of the sign of the
electrostatic contribution is related to the formation of two-dimensional
strongly correlated liquids (SCL) of counterions at the charged surface due to
strong lateral repulsion between them. When a membrane or a polyelectrolyte is
bent, SCL is compressed on one side and stretched on the other so that
thermodynamic properties of SCL contribute to the bending rigidity.
Thermodynamic properties of SCL are similar to those of Wigner crystal and are
anomalous in the sense that the pressure, compressibility and screening radius
of SCL are negative. This brings about substantial negative correction to the
bending rigidity. For the case of DNA this effect qualitatively agrees with
experiment.
