A counter-example to a conjectured characterization of the sphere (Q2708169)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A counter-example to a conjectured characterization of the sphere |
scientific article |
Statements
28 March 2003
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hedgehogs
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convex surface
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surfaces of constant width
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A counter-example to a conjectured characterization of the sphere (English)
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The following conjecture is known: A closed convex surface of class \(C_+^2\) whose principal curvatures \(K_1, K_2\) satisfy NEWLINE\[NEWLINE(K_1 - c)(K_2 -c) \leq 0NEWLINE\]NEWLINE for some constant \(c\) must be a sphere. The conjecture was demonstrated for analytic surfaces of revolution or surfaces which allow a circular orthogonal projection. The author reformulates this conjecture in terms of hedgehogs (in French: herissons) and he gives a counter-example. Besides he proves the conjecture for surfaces of constant width and gives a new proof for analytic surfaces.
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