| 1. | The special case of mean curvature has been proved by Ralph Alexander.
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| 2. | For a minimal surface, the mean curvature is zero at every point.
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| 3. | One interesting property of the unduloid is that the mean curvature is constant.
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| 4. | The mean curvature is parallel to the normal vector.
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| 5. | A surface is a minimal surface if and only if the mean curvature is zero.
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| 6. | This makes the mean curvature zero.
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| 7. | The sphere is the only embedded surface of constant positive mean curvature without boundary or singularities.
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| 8. | The relation between the mean width and the mean curvature is also derived in that reference.
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| 9. | Their proof relied on the machinery of weakly defined inverse mean curvature flow, which they developed.
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| 10. | Sometimes mean curvature is defined by multiplying the sum on the right-hand side by 1 / m.
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