In the context of Rosenfeld's Fundamental Measure Theory, we show that the
bending rigidity is not equal to zero for a hard-sphere fluid in contact with a
curved hard wall. The implication is that the Hadwiger Theorem does not hold in
this case and the surface free energy is given by the Helfrich expansion
instead. The value obtained for the bending rigidity is (1) an order of
magnitude smaller than the bending constant associated with Gaussian curvature,
(2) changes sign as a function of the fluid volume fraction, (3) is independent
of the choice for the location of the hard wall.Comment: 19 pages, 5 figures, to appear in Physical Review
