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
  • [41] Spectral data characterization for the Sturm–Liouville operator on the star-shaped graph
    Natalia P. Bondarenko
    Analysis and Mathematical Physics, 2020, 10
  • [42] Stability of mean convex cones under mean curvature flow
    J. Clutterbuck
    O. C. Schnürer
    Mathematische Zeitschrift, 2011, 267 : 535 - 547
  • [43] Stability of mean convex cones under mean curvature flow
    Clutterbuck, J.
    Schnuerer, O. C.
    MATHEMATISCHE ZEITSCHRIFT, 2011, 267 (3-4) : 535 - 547
  • [44] Delayed stabilization of the Korteweg-de Vries equation on a star-shaped network
    Parada, Hugo
    Crepeau, Emmanuelle
    Prieur, Christophe
    MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS, 2022, 34 (03) : 559 - 605
  • [45] Anisotropic inverse harmonic mean curvature flow
    Lu, Jian
    FRONTIERS OF MATHEMATICS IN CHINA, 2014, 9 (03) : 509 - 521
  • [46] Conformational properties of hybrid star-shaped polymers comprised of linear and ring arms
    Haydukivska, Khristine
    Blavatska, Viktoria
    Klos, Jaroslaw S.
    Paturej, Jaroslaw
    PHYSICAL REVIEW E, 2022, 105 (03)
  • [47] Generalized Mean Curvature Flow in Carnot Groups
    Capogna, Luca
    Citti, Giovanna
    COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2009, 34 (08) : 937 - 956
  • [48] Properness of translating solitons for the mean curvature flow
    Kim, Daehwan
    Pyo, Juncheol
    INTERNATIONAL JOURNAL OF MATHEMATICS, 2022, 33 (04)
  • [49] Mean curvature flow from conical singularities
    Chodosh, Otis
    Daniels-Holgate, J. M.
    Schulze, Felix
    INVENTIONES MATHEMATICAE, 2024, 238 (03) : 1041 - 1066
  • [50] Folate-conjugated amphiphilic star-shaped block copolymers as targeted nanocarriers
    Zhu, Jundong
    Zhou, Zhichao
    Yang, Cuihong
    Kong, Deling
    Wan, Ying
    Wang, Zheng
    JOURNAL OF BIOMEDICAL MATERIALS RESEARCH PART A, 2011, 97A (04) : 498 - 508
12345