The equilibrium shape of hcp He-4 crystals has been studied at tempera
tures 0.05 less than or equal to T less than or equal to 0.7 K by mean
s of a high precision optical interferometer. We find that the profile
of the interfacial boundary, close to an almost horizontal c-facet, h
as a well-defined slope discontinuity separating two angular regions w
ith different behavior of the surface stiffness <(alpha)over tilde>. F
or surfaces tilted by an angle phi less than or equal to 100 mu rad wi
th respect to the c-facet, we obtain <(alpha)over tilde> = k/phi, cont
rary to the linear angular dependence predicted by current theories.