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Stochastic Analysis and Application Research Center

Seminars&Colloquia

  • Colloquium:  Evolution of Crystalline Mean Curvature Flow with a Volume Constraint
  • saarc |
  • 2024-05-08 11:17:47|
  • 137
  • 일시
  • 2024.04.09.(Tue.) 16:00-17:00
  • 장소
  • Rm.1401
  • 연사
  • 권도현 교수
-Title: Evolution of Crystalline Mean Curvature Flow with a Volume Constraint
-Abstract: Atoms and molecules aim to minimize surface energy, while crystals exhibit directional preferences. Starting from the classical isoperimetric problem, we investigate the evolution of volume-preserving crystalline mean curvature flow. Defining a notion of viscosity solutions, we demonstrate the preservation of geometric properties associated with the Wulff shape. We establish global-in-time existence and regularity for a class of initial data. Furthermore, we discuss recent findings on the long-time behavior of the flow towards the critical point of the anisotropic perimeter functional in a planar setting.
 
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