  We study the evolution of star-shaped sets in volume preserving mean
curvature flow. Constructed by approximate minimizing movements, our solutions
preserve a strong version of star-shapedness. We also show that the solutions
converges to a ball as time goes to infinity. For asymptotic behavior of the
solutions we use the gradient flow structure of the problem, whereas a modified
notion of viscosity solutions is introduced to study the geometric properties
of the flow by moving planes method.
