On a necessary condition for spanners in a wedge

Sung-ho Park

Vol. 234 (2008), No. 1, 161–165

DOI: 10.2140/pjm.2008.234.161

Abstract

A spanner in a wedge or in a triangular pyramid is a compact embedded surface of constant mean curvature that does not meet the edge of the wedge or the triangular pyramid and meets the planes at constant angles. We show that the area of the planar region bounded by the boundary curve(s) on each plane, which is called the wetted region, of a spanner should be bigger than or equal to the area of the wetted region of the unique spherical spanner.

Keywords

capillary surfaces, balancing formula, spanner

Mathematical Subject Classification 2000

Primary: 53A05, 53A10

Milestones

Received: 7 March 2007

Revised: 28 July 2007

Published: 1 January 2008