Motion by crystalline-like mean curvature: a survey

TL;DR

This survey reviews crystalline curvature flows, focusing on their mathematical properties and the well-posedness of their initial value problems in the context of anisotropic curvature evolution.

Contribution

It provides a comprehensive overview of crystalline curvature flows, highlighting recent advances and open problems in their mathematical analysis.

Findings

Summarizes key results on well-posedness of crystalline curvature flows.

Identifies main challenges in analyzing anisotropic curvature evolution.

Outlines future research directions in the field.

Abstract

We consider a class of anisotropic curvature flows called a crystalline curvature flow. We present a survey on this class of flows with special emphasis on the well-posedness of its initial value problem.