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Conformal Geometry and Dynamics

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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
DOI: https://doi.org/10.1090/ecgd/283
Published electronically: October 28, 2015
MathSciNet review: 3416311
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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
Email: chady.mir@gmail.com

Zeina Yassine
Affiliation: Laboratoire D’analyse et Mathématiques Appliquées (UMR 8050), Université Paris-Est, UPEC, UPEMLV, CNRS, F-94010, Créteil, France
Email: zeina.yassine@u-pec.fr

DOI: https://doi.org/10.1090/ecgd/283
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

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