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arXiv · 2103.02865

A Pu-Bonnesen inequality

Mikhail G. Katz·Stephane Sabourau
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Abstract

We prove an inequality of Bonnesen type for the real projective plane, generalizing Pu's systolic inequality for positively-curved metrics. The remainder term in the inequality, analogous to that in Bonnesen's inequality, is a function of R-r (suitably normalized), where R and r are respectively the circumradius and the inradius of the Weyl-Lewy Euclidean embedding of the orientable double cover. We exploit John ellipsoids of a convex body and Pogorelov's ridigity theorem.

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Mikhail G. Katz, Stephane Sabourau. 2021-03-04. A Pu-Bonnesen inequality. https://arxiv.org/abs/2103.02865

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