A systolic inequality with remainder in the real projective plane-Reference-Cited by-同舟云学术

A systolic inequality with remainder in the real projective plane

Published:2020-01-01 Issue:1 Volume:18 Page:902-906
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Katz Mikhail G.¹,Nowik Tahl¹

Affiliation:

1. Department of Mathematics, Bar Ilan University , Ramat Gan 5290002 , Israel

Abstract

Abstract 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.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/math-2020-0050/pdf

Reference18 articles.

1. Pao Ming Pu, Some inequalities in certain nonorientable Riemannian manifolds, Pacific J. Math. 2 (1952), 55–71.

2. Mikhael Gromov, Filling Riemannian manifolds, J. Differ. Geom. 18 (1983), no. 1, 1–147.

3. Mikhael Gromov, Metric structures for Riemannian and non-Riemannian spaces, Based on the 1981 French original with appendices by M. Katz, P. Pansu and S. Semmes, Translated from the French by S. M. Bates, Progress in Mathematics, 152, Birkhäuser Boston, Boston, MA, 1999.

4. Marcel Berger, Lectures on Geodesics in Riemannian Geometry, Tata Institute of Fundamental Research Lectures on Mathematics, No. 33, Tata Institute of Fundamental Research, Bombay, 1965.

5. Charles Horowitz, Karin Usadi Katz, and Mikhail Katz, Loewner’s torus inequality with isosystolic defect, J. Geom. Anal. 19 (2009), no. 4, 796–808.

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