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arXiv · 1904.07824

Distortion of spheres and surfaces in space

Sebastian Baader·Luca Studer·Roger Züst
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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 minimisers 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.

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Sebastian Baader, Luca Studer, Roger Züst. 2019-04-16. Distortion of spheres and surfaces in space. https://arxiv.org/abs/1904.07824

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