On volume-preserving crystalline mean curvature flow

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 exi...

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Bibliographic Details
Published in:arXiv.org 2020-12
Main Authors: Kim, Inwon, Kwon, Dohyun, Požár, Norbert
Format: Article
Language:English
Subjects:
Crystal structure
Crystallinity
Curvature
Online Access:Get full text
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Summary: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.
ISSN:2331-8422