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.

Glen Wheeler

Valentina-Mira Wheeler

Communications in Analysis and Geometry

发表与经典分析、偏微分方程、代数几何、微分几何和拓扑相关的高质量论文。

The journal "Communications in Analysis and Geometry" publishes high-quality research papers related to classical analysis, partial differential equations, algebraic geometry, differential geometry, and topology.

《Communications in Analysis and Geometry》期刊发表与经典分析、偏微分方程、代数几何、微分几何和拓扑相关的高质量研究论文。

Category	Quartile
数学	4
数学, 数学	4

Curve diffusion and straightening flows on parallel lines

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