Grim Raindrop: A Translating Solution to Curve Diffusion Flow
arXiv:2412.15934
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 \[ \left( \frac{dX}{dt}\right) ^{\perp}=-κ_{ss}N. \]