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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.

DISTORTION OF SPHERES AND SURFACES IN SPACE