  We construct some examples of special Lagrangian submanifolds and Lagrangian
self-similar solutions in almost Calabi-Yau cones over toric Sasaki manifolds.
For example, for any integer g>0, we can construct a real 6 dimensional
Calabi-Yau cone M_g and a 3 dimensional special Lagrangian submanifold L^1_g in
M_g which is diffeomorphic to the product of a closed surface of genus g and
the real line R, and a 3 dimensional compact Lagrangian self-shrinker L^2_g in
M_g which is diffeomorphic to the product of the closed surface of genus g and
a circle S^1.
