Vol. 225, No. 1, 2006

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Characterization of Cheeger sets for convex subsets of the plane

Bernd Kawohl and Thomas Lachand-Robert

Vol. 225 (2006), No. 1, 103–118
Abstract

Given a planar convex domain Ω, its Cheeger set 𝒞Ω is defined as the unique minimizer of |∂X||X| among all nonempty open and simply connected subsets X of Ω. We prove an interesting geometric property of 𝒞Ω, characterize domains Ω which coincide with 𝒞Ω and provide a constructive algorithm for the determination of 𝒞Ω.

Keywords
Cheeger constant, Cheeger set, convexity, constructive algorithm, connection-like coycle
Mathematical Subject Classification 2000
Primary: 52A40, 49Q20, 28A75
Milestones
Received: 10 August 2004
Revised: 15 March 2005
Accepted: 24 March 2005
Published: 1 May 2006
Authors
Bernd Kawohl
Mathematisches Institut
Universität zu Köln
D 50923 Köln
Germany
http://www.mi.uni-koeln.de/~kawohl
†Thomas Lachand-Robert
Laboratoire de mathématiques
Université de Savoie
73376 Le Bourget-du-lac
France