Isoperimetric inequalities for sectors on surfaces

Hyoungsick Bahn and Sungpyo Hong

Vol. 196 (2000), No. 2, 257–270

DOI: 10.2140/pjm.2000.196.257

Abstract

We discuss sectors on a surface of curvature bounded above by a constant and derive an isoperimetric inequality for a proper sector on such a surface. With this isoperimetric inequality we derive an inequality involving the total length of the cut locus of a point on a closed surface.

Milestones

Received: 10 March 1999

Revised: 23 June 1999

Published: 1 December 2000