  We compare the roughness of minimal energy(ME) surfaces and scalar
``quasi-static'' fracture surfaces(SQF). Two dimensional ME and SQF surfaces
have the same roughness scaling, w sim L^zeta (L is system size) with zeta =
2/3. The 3-d ME and SQF results at strong disorder are consistent with the
random-bond Ising exponent zeta (d >= 3) approx 0.21(5-d) (d is bulk
dimension). However 3-d SQF surfaces are rougher than ME ones due to a larger
prefactor. ME surfaces undergo a ``weakly rough'' to ``algebraically rough''
transition in 3-d, suggesting a similar behavior in fracture.
