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arXiv · 2412.15934

Grim Raindrop: A Translating Solution to Curve Diffusion Flow

W. Jacob Ogden·Micah Warren
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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 \[ \left( \frac{dX}{dt}\right) ^{\perp}=-\kappa_{ss}N. \]

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W. Jacob Ogden, Micah Warren. 2024-12-20. Grim Raindrop: A Translating Solution to Curve Diffusion Flow. https://arxiv.org/abs/2412.15934

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