Isosystolic genus three surfaces critical for slow metric variations

Sabourau, Stéphane

doi:10.2140/gt.2011.15.1477

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Isosystolic genus three surfaces critical for slow metric variations

Stéphane Sabourau

Geometry & Topology 15 (2011) 1477–1508

DOI: 10.2140/gt.2011.15.1477

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

Volume 15, issue 3 (2011)