An equality for the curvature function of a simple and closed curve on the plane
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 b...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2003-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171203210371 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |