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Some remarks about
closed convex curves
Ke Ou and Shengliang Pan |
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Vol. 248 (2010), No. 2, 393–401
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Abstract |
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We introduce a function wk(𝜃) for closed convex plane curves, and then prove a geometric inequality involving wk(𝜃) and the area A enclosed by the curve. As a by-product, we give a new proof of the classical isoperimetric inequality. Finally, we give some properties of convex curves with wk(𝜃) being constant and pose an open problem motivated by the elegant Blaschke–Lebesgue theorem. |
Keywords
closed convex plane curves, Minkowski’s support function,
geometric inequality
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Mathematical Subject Classification 2000
Primary: 52A38
Secondary: 52A40
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Milestones
Received: 10 September 2009
Revised: 13 November 2009
Accepted: 11 December 2009
Published: 1 December 2010
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Authors |
| Ke Ou | |
| Department of Mathematics, East China Normal University Shanghai 200241 China |
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| Shengliang Pan | |
| Department of Mathematics Tongji University Shanghai 200092 China |
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