Seminars&Colloquia
- Colloquium: Evolution of Crystalline Mean Curvature Flow with a Volume Constraint
- saarc |
- 2024-05-08 11:17:47|
- 189
- 2024-05-08 11:17:47|
- 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.
-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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