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Showing 1 to 4 of 4 for “"total curvature"”.
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Curves, Knots, and Total Curvature
… exposition of various results dealing with the total curvature of curves in Euclidean 3-space. There are two primary results: Fenchel's theorem and the theorem of Fary and Milnor. Fenchel's theorem states that the total curvature of a simple closed curve is greater than or equal to $2\pi$, with …
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Extremal Problems for Curves in Metric Spaces of Curvature Bounded Above
We consider extremal problems involving curvature and curve length in metric spaces of curvature bounded above in the sense of Alexandrov. To a large extent, these problems have previously been solved only in Euclidean space. In addition to a nontrivial extention of the definition of total …
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Alternating Quadrisecants of Knots
… to two previously known theorems about the total curvature and second hull of knotted curves. Moreover, essential alternating quadrisecants may be used to dramatically improve the known lower bounds on the ropelength of thick knots.
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Solid-state superionic conductors for advanced nanoscale fabrication
… stamp holder had a large effect on the overall curvature of the final stamp. This characterization leads to the ability to fabricate stamps with less than 200nm total curvature across a 4mm diameter of the stamp. While working with AgIAgPO3, the clarity needed for optically imaging through the …