Isosystolic genus three surfaces critical for slow metric variations

Stéphane Sabourau

doi:10.2140/gt.2011.15.1477

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Home > Journals > Geom. Topol. > Volume 15 > Issue 3 > Article

2011 Isosystolic genus three surfaces critical for slow metric variations

Stéphane Sabourau

Geom. Topol. 15(3): 1477-1508 (2011). DOI: 10.2140/gt.2011.15.1477

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Abstract

We show that the two piecewise flat surfaces with conical singularities conjectured by E Calabi as extremal surfaces for the isosystolic problem in genus $3$ are critical with respect to some metric variations. The proof relies on a new approach to study isosystolic extremal surfaces.

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Stéphane Sabourau. "Isosystolic genus three surfaces critical for slow metric variations." Geom. Topol. 15 (3) 1477 - 1508, 2011. https://doi.org/10.2140/gt.2011.15.1477

Information

Received: 4 March 2010; Revised: 26 June 2011; Accepted: 12 June 2011; Published: 2011

First available in Project Euclid: 20 December 2017

zbMATH: 1246.53061

MathSciNet: MR2825317

Digital Object Identifier: 10.2140/gt.2011.15.1477

Subjects:

Primary: 53C23

Secondary: 53C20 , 53C22 , 53C38

Keywords: Busemann function , Calabi surface , Calibration , extremal surface , flat surface with conical singularities , systole , systolic inequality

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