Periodic Rotating Waves of a Geodesic Curvature Flow on the Sphere |
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Authors: | Bendong Lou |
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Affiliation: | 1. Department of Mathematics , Tongji University , Shanghai, China blou@mail.tongji.edu.cn |
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Abstract: | Given a zone on the unit sphere S2 with periodic undulating boundaries, we consider the motion of a curve in this zone which is driven by its geodesic curvature. First, we give a necessary and sufficient condition for the existence of periodic rotating waves. Then we study how the average rotating speed of the periodic rotating wave depends on the geometry of the boundaries. We find that when the period of the boundaries tends to 0, the homogenization limit of the rotating speed depends only on the maximum slope of the domain boundaries. |
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Keywords: | Geodesic curvature flow Homogenization limit Periodic rotating waves |
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