A Class of Convex Curves Arising in Capillary Floating Problem

Shilun Li Guangdong Experimental High School

S.-T. Yau High School Science Awarded Papers mathscidoc:1702.35013

Motivated by Gutkin curves arising in capillary floating and billiard ball problem, we introduce a new projection function for convex plane curves, and study the curves when the defined projection function is constant. These curves can be regarded as a generalization of curves with constant width. We give a necessary and sufficient condition for the existence of such curves, and provide an explicit expression for the radius of curvature. Properties of our curves and their relation to Gutkin curves are also discussed. Finally, we construct and exhibit some curves with constant projection function.
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  title={A Class of Convex Curves Arising in Capillary Floating Problem},
  author={Shilun Li},
Shilun Li. A Class of Convex Curves Arising in Capillary Floating Problem. 2016. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170227160120377067533.
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