Generalized crystalline evolutions as limits of flows with smooth anisotropies

TL;DR

This paper establishes the existence and uniqueness of weak solutions for anisotropic and crystalline mean curvature flows by analyzing their limits from smooth anisotropic flows, advancing understanding of geometric evolution equations.

Contribution

It introduces a novel approach to analyze crystalline mean curvature flows as limits of smooth anisotropic flows, providing rigorous proof of existence and uniqueness.

Findings

Weak solutions exist and are unique for anisotropic and crystalline mean curvature flows.

Crystalline flows can be obtained as limits of flows with smooth anisotropies.

The approach bridges smooth and crystalline geometric evolutions.

Abstract

We prove existence and uniqueness of weak solutions to anisotropic and crystalline mean curvature flows, obtained as limit of the viscosity solutions to flows with smooth anisotropies.