Limit shape of the cross-section of shrinking doughnuts (Q1309208)
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scientific article; zbMATH DE number 469079
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Limit shape of the cross-section of shrinking doughnuts |
scientific article; zbMATH DE number 469079 |
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Limit shape of the cross-section of shrinking doughnuts (English)
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8 March 1994
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We discuss the asymptotic behaviour of symmetric tori which are shrinking to a circle by the mean curvature flow. Employing the backward heat kernel analysis we show that the limit shape of its cross-section is a circle. The assumption we set is that the isoperimetric ratio of the generating curve remains bounded as shrinking, which follows in particular from the convexity of curves.
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asymptotic behaviour
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singularities
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mean curvature flow
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isoperimetric ratio
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