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

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