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Tightness and Curvature |
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Note that
{1\over 2\pi} \int_M |K|\,dx \ge \left|{1\over 2\pi} \int_M K\,dx\right|
is a strict inequality only when K takes on both
positive and negative values.
Theorem: a surface in a CES is tight if, and only if, its curvature does not change sign. |
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