DISTORTION OF SPHERES AND SURFACES IN SPACE
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Abstract It is known that the surface of a cone over the unit disc with large height has smaller distortion than the standard embedding of the 2-sphere in $\mathbb{R}^3$. In this note we show that distortion minimizers exist among convex embedded 2-spheres and have uniformly bounded eccentricity. Moreover, we prove that $\pi /2$ is a sharp lower bound on the distortion of embedded closed surfaces of positive genus.
1991 ◽
Vol 14
(4)
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pp. 821-823
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2016 ◽
Vol 41
(4)
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pp. 2011-2018
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2015 ◽
Vol 91
(3)
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pp. 353-367
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