Area, width, and logarithmic capacity of convex sets

Roger W. Barnard, Kent Pearce and Alexander Yu. Solynin

Vol. 212 (2003), No. 1, 13–24

DOI: 10.2140/pjm.2003.212.13

Abstract

For a planar convex compact set E, we describe the mutual range of its area, width, and logarithmic capacity. This result will follow from a more general theorem describing the mutual range of area, logarithmic capacity, and length of orthogonal projection onto a given axis of an arbitrary compact set, connected or not.

Milestones

Received: 20 May 2002

Published: 1 November 2003