Speed estimate for a periodic rotating wave in an undulating zone on the sphere

Abstract

On the unit sphere $S^2$ given a zone with periodically undulating boundaries, we consider periodic rotating waves (curves) in this zone which are driven by geodesic curvature. We state without proof the existence of periodic rotating waves. Then we study how the average rotating speed depends on the geometry of the boundaries, give the estimate of this average speed by using its homogenization limit.