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.
Original language | English |
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Article number | 18 |
Journal | Journal of Geometry |
Volume | 112 |
Issue number | 2 |
DOIs | |
State | Published - Aug 2021 |
Bibliographical note
Publisher Copyright:© 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
Keywords
- Bonnesen’s inequality
- Circumscribed and inscribed radii
- Convex surfaces
- Pu’s inequality