The classification of constant weighted curvature curves in the plane with a log-linear density

Doan The Hieu; Tran Le Nam

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arXiv · 1312.7388

The classification of constant weighted curvature curves in the plane with a log-linear density

Doan The Hieu·Tran Le Nam

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Abstract

In this paper, we classify the class of constant weighted curvature curves in the plane with a log-linear density, or in other words, classify all traveling curved fronts with a constant forcing term in $\Bbb R^2.$ The classification gives some interesting phenomena and consequences including: the family of curves converge to a round point when the weighted curvature of curves (or equivalently the forcing term of traveling curved fronts) goes to infinity, a simple proof for a main result in [13] as well as some well-known facts concerning to the isoperimetric problem in the plane with density $e^y.$

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Doan The Hieu, Tran Le Nam. 2013-12-28. The classification of constant weighted curvature curves in the plane with a log-linear density. https://arxiv.org/abs/1312.7388

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