论文标题
在体积保存的晶体平均曲率流上
On volume-preserving crystalline mean curvature flow
论文作者
论文摘要
在这项工作中，我们考虑了在非凸面设置中的整体存在晶体曲率流的全球存在。我们表明，与流动相关的自然几何特性与沃尔夫形状的反射对称性相关。使用这种几何特性，我们解决了平滑各向异性的流动的全局存在和规律性。对于非平滑案例，我们为已知已知全球范围的各向异性类型建立了全球存在结果。
In this work we consider the global existence of volume-preserving crystalline curvature flow in a non-convex setting. We show that a natural geometric property, associated with reflection symmetries of the Wulff shape, is preserved with the flow. Using this geometric property, we address global existence and regularity of the flow for smooth anisotropies. For the non-smooth case we establish global existence results for the types of anisotropies known to be globally well-posed.
