A systolic inequality with remainder in the real projective plane

A systolic inequality with remainder in the real projective plane

The first paper in systolic geometry was published by Loewner’s student P. M. Pu over half a century ago. Pu proved an inequality relating the systole and the area of an arbitrary metric in the real projective plane. We prove a stronger version of Pu’s systolic inequality with a remainder term.

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Bibliographische Detailangaben
Veröffentlicht in:Open mathematics (Warsaw, Poland) Poland), 2020-08, Vol.18 (1), p.902-906
Hauptverfasser: Katz, Mikhail G., Nowik, Tahl
Format: Artikel
Sprache:eng
Schlagworte:
53A30
53C23
Cauchy-Schwarz theorem
geometric inequality
Inequality
probabilistic variance
Riemannian submersion
Systole
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Zusammenfassung:The first paper in systolic geometry was published by Loewner’s student P. M. Pu over half a century ago. Pu proved an inequality relating the systole and the area of an arbitrary metric in the real projective plane. We prove a stronger version of Pu’s systolic inequality with a remainder term.
ISSN:2391-5455
2391-5455
DOI:10.1515/math-2020-0050