Work

Grim raindrop: A translating solution to curve diffusion flow

Year: 2025

Type: article

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 ( d X d t ) ⊥ = − κ s s N . \begin{equation*} \left ( \frac {dX}{dt}\right ) ^{\perp }=-\kappa _{ss}N. \end{equation*}

Source: Proceedings of the American Mathematical Society

DOI: 10.1090/proc/17505

Authors: W. Ogden, Micah Warren

Institutions: University of Washington, University of Oregon

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Award: G653274256