Volume preserving mean curvature flow for star-shaped sets

被引：13
|
作者：
Kim, Inwon [1 ]
Kwon, Dohyun [1 ]
机构：
[1] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90024 USA
来源：
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2020年 / 59卷 / 02期
关键词：
35K55; 35D40; 35K93; 53C44; 2ND-ORDER PARABOLIC EQUATIONS; VISCOSITY SOLUTIONS; L-1; DEPENDENCE; EXISTENCE; STABILITY; TIME;
D O I：
10.1007/s00526-020-01738-0
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
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页数：40
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