Inequalities for the curvature of curves and surfaces (Q941781)
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scientific article; zbMATH DE number 5319270
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Inequalities for the curvature of curves and surfaces |
scientific article; zbMATH DE number 5319270 |
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Inequalities for the curvature of curves and surfaces (English)
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2 September 2008
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This article discusses bounds for the total mean curvature of two closed surfaces in 3-space of same topology in terms of their total absolute curvatures and their Fréchet distance. This result also applies to bound the difference of the lengths of two curves. Using methods from algebraic topology the difference of the total mean curvatures of two surfaces can be obtained without bounds for the angles of their normals. This result applies also to estimate the total mean curvature of a smooth surface from a piecewise-linear approximation.
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topological persistence
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stability
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curvature
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Fréchet spaces
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integral geometry
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bottleneck distance
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approximation
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