On the \(\frac 12\)-problem of Besicovitch: quasi-arcs do not contain sharp saw-teeth (Q699247)
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scientific article; zbMATH DE number 1803982
| Language | Label | Description | Also known as |
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| English | On the \(\frac 12\)-problem of Besicovitch: quasi-arcs do not contain sharp saw-teeth |
scientific article; zbMATH DE number 1803982 |
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On the \(\frac 12\)-problem of Besicovitch: quasi-arcs do not contain sharp saw-teeth (English)
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24 November 2002
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According to Besicovitch's 1/2-conjecture, the lower spherical densities of a totally unrectifiable 1-set in the plane are typically bounded above by 1/2. In [Adv. Math. 149, No. 1, 89-129 (2000; Zbl 0946.28001)] the author proved this conjecture under an additional flatness assumption. In the present paper he develops new and simpler methods, based on general properties of finite sets, to prove the same result.
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unrectifiable set
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1/2-problem of Besicovitch
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rectifiable set
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density
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quasi arc
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Hausdorff measure
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