Calculus of Variations and Geometric Measure Theory

D. Krejcirik - A. Pratelli

The Cheeger constant of curved strips

created by pratelli on 15 Nov 2010
modified on 16 Feb 2015


Published Paper

Inserted: 15 nov 2010
Last Updated: 16 feb 2015

Journal: Pacific J. Math
Year: 2010


We study the Cheeger constant and Cheeger set for domains obtained as strip-like neighbourhoods of curves in the plane. If the reference curve is complete and finite (a ``curved annulus''), then the strip itself is a Cheeger set and the Cheeger constant equals the inverse of the half-width of the strip. The latter holds true for unbounded strips as well, but there is no Cheeger set. Finally, for strips about non-complete finite curves, we derive lower and upper bounds to the Cheeger set, which become sharp for infinite curves. The paper is concluded by numerical results for circular sectors.