The Cheeger constant of curved strips

Details The Cheeger constant of curved strips The Cheeger constant of curved strips

2010-11-15

arxiv.org/abs/1011.3490v2

Pacific J. Math. 254 (2011), 309-333

Mathematics

Optimization and Control

18 pages, 22 figures; typos and a gap in the proof of Lemma 6 corrected

Scientific paper

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.

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