An Equality for the Curvature Function of a Simple and Closed Curve on the Plane
نویسنده
چکیده
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 Riemannmapping 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.
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