Volume preserving mean curvature flow for star-shaped sets
Volume preserving mean curvature flow for star-shaped sets
复制标题
星形集的体积保持平均曲率流
DOI：
10.1007/s00526-020-01738-0
复制
发表时间：
2018
影响因子：
2.1
通讯作者：
Dohyun Kwon
中科院分区：
文献类型：
--
作者：
Inwon C. Kim;Dohyun Kwon
我们研究了体积保持平均曲率流中星形集的演化。通过近似最小化运动构建，我们的解决方案保留了强烈的星形版本。我们还证明了随着时间的推移，解收敛到一个球。对于解的渐近行为，我们使用问题的梯度流结构，而引入了修正的粘性解的概念，用移动平面法研究流的几何性质。
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.