English

Grim Raindrop: A Translating Solution to Curve Diffusion Flow

Differential Geometry 2024-12-23 v1 Analysis of PDEs

Abstract

We show the existence of a properly immersed translating solution to curve diffusion flow in the plane. Curve diffusion flow is a higher order version of curve shortening flow, namely (dXdt)=κssN. \left( \frac{dX}{dt}\right) ^{\perp}=-\kappa_{ss}N.

Keywords

Cite

@article{arxiv.2412.15934,
  title  = {Grim Raindrop: A Translating Solution to Curve Diffusion Flow},
  author = {W. Jacob Ogden and Micah Warren},
  journal= {arXiv preprint arXiv:2412.15934},
  year   = {2024}
}
R2 v1 2026-06-28T20:43:53.159Z