Affine Subspaces of Curvature Functions from Closed Planar Curves.
Leonardo AlesePublished in: Results in mathematics (2021)
Given a pair of real functions (k, f), we study the conditions they must satisfy for k + λ f to be the curvature in the arc-length of a closed planar curve for all real λ . Several equivalent conditions are pointed out, certain periodic behaviours are shown as essential and a family of such pairs is explicitely constructed. The discrete counterpart of the problem is also studied.
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