Volume preserving mean curvature flow for star-shaped sets

Inwon Kim, Dohyun Kwon

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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 languageEnglish
Article number81
JournalCalculus of Variations and Partial Differential Equations
Issue number2
StatePublished - 1 Apr 2020


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