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Isosystolic genus three surfaces critical for slow metric variations

Stéphane Sabourau

Geometry & Topology 15 (2011) 1477–1508
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.

Keywords
systole, systolic inequality, extremal surface, flat surface with conical singularities, Calabi surface, calibration, Busemann function
Mathematical Subject Classification 2000
Primary: 53C23
Secondary: 53C20, 53C22, 53C38
References
Publication
Received: 4 March 2010
Revised: 26 June 2011
Accepted: 12 June 2011
Published: 3 August 2011
Proposed: Dmitri Burago
Seconded: Tobias H. Colding, Leonid Polterovich
Authors
Stéphane Sabourau
Laboratoire de Mathématiques et Physique Théorique
Université François-Rabelais Tours
Parc de Grandmont
37200 Tours
France
http://www.lmpt.univ-tours.fr/~sabourau