Isoperimetric surfaces with boundary, II

Abraham Frandsen, Donald Sampson and Neil Steinburg

Vol. 259 (2012), No. 2, 307–313

DOI: 10.2140/pjm.2012.259.307

Abstract

Following our previous work with Dorff and Lawlor, we extend results for the so-called equitent problem of fixed boundary and fixed volume. We define sufficient conditions, which in ℝ² and ℝ³ are also necessary, for local minima to be piecewise spherical, and we show that these are area-minimizing in their homotopy class. We also give new examples of these surfaces in ℝ² and ℝ³.

Keywords

metacalibration, calibration, isoperimetric, equitent

Mathematical Subject Classification 2010

Primary: 53C38

Secondary: 49Q10

Milestones

Received: 26 January 2012

Accepted: 22 June 2012

Published: 3 October 2012