Volume preserving mean curvature flow for star-shaped sets
Analysis of PDEs
2018-08-16 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1808.04922,
title = {Volume preserving mean curvature flow for star-shaped sets},
author = {Inwon Kim and Dohyun Kwon},
journal= {arXiv preprint arXiv:1808.04922},
year = {2018}
}