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
收藏
页数：40
相关论文
共 50 条
  • [21] DISPERSIVE WAVES WITH MULTIPLE TUNNEL EFFECT ON A STAR-SHAPED NETWORK
    Mehmeti, F. Ali
    Haller-Dintelmann, R.
    Regnier, V.
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2013, 6 (03): : 783 - 791
  • [22] Resonance identities and stability of symmetric closed characteristics on symmetric compact star-shaped hypersurfaces
    Liu, Hui
    Long, Yiming
    CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2015, 54 (04) : 3753 - 3787
  • [23] Hydrogels assembled from star-shaped polypeptides with a dendrimer as the core
    Shen, Yong
    Zhang, Shusheng
    Wan, Yaoming
    Fu, Wenxin
    Li, Zhibo
    SOFT MATTER, 2015, 11 (15) : 2945 - 2951
  • [24] Morphological selectivity of the films of linear and star-shaped poly (ε-caprolactone)
    Bhayo, Adnan Murad
    Rahim, Sana
    Durrani, Sidra Safdar
    Iftikhar, Faiza Jan
    Shah, Muhammad Raza
    Ul-Hamid, Anwar
    Malik, Muhammad Imran
    JOURNAL OF MATERIALS SCIENCE, 2021, 56 (12) : 7334 - 7347
  • [25] Star-Shaped MePEGn Polymers as H+ Conducting Electrolytes
    Sun, Chengjun
    Ritchie, Jason E.
    JOURNAL OF PHYSICAL CHEMISTRY B, 2011, 115 (26) : 8381 - 8389
  • [26] Shape Matters: Comprehensive Analysis of Star-Shaped Lipid Nanoparticles
    Cao, Shuwen
    Liu, Xiaodi
    Li, Xiuling
    Lin, Chunhao
    Zhang, Wenyue
    Tan, Chee Hwee
    Liang, Shunung
    Luo, Baoming
    Xu, Xiaoding
    Saw, Phei Er
    FRONTIERS IN PHARMACOLOGY, 2020, 11
  • [27] Evolution of contractions by mean curvature flow
    Savas-Halilaj, Andreas
    Smoczyk, Knut
    MATHEMATISCHE ANNALEN, 2015, 361 (3-4) : 725 - 740
  • [28] Motion of level sets by inverse anisotropic mean curvature
    Della Pietra, Francesco
    Gavitone, Nunzia
    Xia, Chao
    COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 2023, 31 (01) : 97 - 118
  • [29] A dichotomy result for closed characteristics on compact star-shaped hypersurfaces in R2n
    Duan, Huagui
    Liu, Hui
    Ren, Wenyan
    MATHEMATISCHE ZEITSCHRIFT, 2022, 302 (02) : 743 - 757
  • [30] Multiplicity and ellipticity of closed characteristics on compact star-shaped hypersurfaces in R2n
    Duan, Huagui
    Liu, Hui
    CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2017, 56 (03)
12345