An equality for the curvature function of a simple and closed curve on the plane

Biao Ou

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-8

Abstract:

We prove an equality for the curvature function of a simple and closed curve on the plane. This equality leads to another proof of the four-vertex theorem in differential geometry. While examining the regularity assumption on the curve for the equality, we make comments on the relation between the boundary regularity of a Riemann mapping and two important subjects, the Schauder theory and the strong maximum principle, for elliptic partial differential equations of second order. We take a note on the curvature function itself in recognizing people's handwriting by a calculating device, as an afterthought on the equality.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:341941

DOI: 10.1155/S0161171203210371

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