Curve diffusion and straightening flows on parallel lines

Glen Wheeler; Valentina-Mira Wheeler

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arXiv · 1703.10711

Curve diffusion and straightening flows on parallel lines

Glen Wheeler·Valentina-Mira Wheeler

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Abstract

In this paper, we study families of immersed curves $\gamma:(-1,1)\times[0,T)\rightarrow\mathbb{R}^2$ with free boundary supported on parallel lines $\{\eta_1, \eta_2\}:\mathbb{R}\rightarrow\mathbb{R}^2$ evolving by the curve diffusion flow and the curve straightening flow. The evolving curves are orthogonal to the boundary and satisfy a no-flux condition. We give estimates and monotonicity on the normalised oscillation of curvature, yielding global results for the flows.

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Glen Wheeler, Valentina-Mira Wheeler. 2017-03-30. Curve diffusion and straightening flows on parallel lines. https://arxiv.org/abs/1703.10711

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