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.

引用

页数：40

共 50 条

[31] Consistency of the Flat Flow Solution to the Volume Preserving Mean Curvature Flow
Julin, Vesa
Niinikoski, Joonas
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2024, 248 (01)
[32] Volume-preserving flow by powers of the mth mean curvature
Cabezas-Rivas, Esther
Sinestrari, Carlo
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2010, 38 (3-4) : 441 - 469
[33] Nonlocal estimates for the volume preserving mean curvature flow and applications
Lambert, Ben
Maeder-Baumdicker, Elena
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2023, 62 (07)
[34] Volume-preserving flow by powers of the mth mean curvature
Esther Cabezas-Rivas
Carlo Sinestrari
Calculus of Variations and Partial Differential Equations, 2010, 38 : 441 - 469
[35] THE VOLUME-PRESERVING MEAN CURVATURE FLOW IN EUCLIDEAN SPACE
Li, Haozhao
PACIFIC JOURNAL OF MATHEMATICS, 2009, 243 (02) : 331 - 355
[36] Nonlocal estimates for the volume preserving mean curvature flow and applications
Ben Lambert
Elena Mäder-Baumdicker
Calculus of Variations and Partial Differential Equations, 2023, 62
[37] A Volume-Preserving Anisotropic Mean Curvature Type Flow
Wei, Yong
Xiong, Changwei
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2021, 70 (03) : 881 - 905
[38] Motion by volume preserving mean curvature flow near cylinders
Hartley, David
COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 2013, 21 (05) : 873 - 889
[39] Singularities of axially symmetric volume preserving mean curvature flow
Athanassenas, Maria
Kandanaarachchi, Sevvandi
COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 2022, 30 (08) : 1683 - 1711
[40] Optimal control of volume-preserving mean curvature flow
Laurain, Antoine
Walker, Shawn W.
JOURNAL OF COMPUTATIONAL PHYSICS, 2021, 438

← 1 2 3 4 5 →