Abstract
We study the evolution of star-shaped sets in volume preserving mean curvature flow. Constructed by approximate minimizing movements, our solution preserves a strong version of star-shapedness. We also show that the solution converges to a ball as time goes to infinity. For asymptotic behavior of the solution 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.
| Original language | English |
|---|---|
| Article number | 81 |
| Journal | Calculus of Variations and Partial Differential Equations |
| Volume | 59 |
| Issue number | 2 |
| DOIs | |
| State | Published - 1 Apr 2020 |