Anisotropic curvature flow of immersed curves

TL;DR

This paper proves the short-time existence of solutions to the anisotropic and crystalline curvature flow for immersed planar curves, advancing the mathematical understanding of such geometric evolutions.

Contribution

It establishes the existence of { extphi}-regular solutions to anisotropic and crystalline curvature flow, a significant step in geometric analysis.

Findings

Proved short-time existence of solutions

Established { extphi}-regularity conditions

Advanced understanding of anisotropic curvature flows

Abstract

We prove short-time existence of {\phi}-regular solutions to the anisotropic and crystalline curvature flow of immersed planar curves.