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Conformal Geometry and Dynamics

ISSN 1088-4173



Conformal geometric inequalities on the Klein bottle

Authors: Chady El Mir and Zeina Yassine
Journal: Conform. Geom. Dyn. 19 (2015), 240-257
MSC (2010): Primary 53C20, 53C22, 53C23
Published electronically: October 28, 2015
MathSciNet review: 3416311
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove three optimal conformal geometric inequalities of
C. Blatter type on every Riemannian Klein bottle. These inequalities provide conformal lower bounds on the area and involve lengths of homotopy classes of curves that are natural candidates to realize the systole.

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Additional Information

Chady El Mir
Affiliation: Laboratoire de Mathématiques et Applications (LaMA), Université Libanaise, Tripoli, Liban

Zeina Yassine
Affiliation: Laboratoire D’analyse et Mathématiques Appliquées (UMR 8050), Université Paris-Est, UPEC, UPEMLV, CNRS, F-94010, Créteil, France

Keywords: Klein bottle, conformal metric, systole, isosystolic inequality
Received by editor(s): April 17, 2014
Received by editor(s) in revised form: November 8, 2015, August 16, 2015, and September 4, 2015
Published electronically: October 28, 2015
Article copyright: © Copyright 2015 American Mathematical Society