%0 Journal Article
%T The Cheeger constant of curved strips
%A David Krejcirik
%A Aldo Pratelli
%J Mathematics
%D 2010
%I arXiv
%X 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.
%U http://arxiv.org/abs/1011.3490v2