We study the Cheeger constant and Cheeger set for domains obtained as strip-like neighborhoods 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 noncomplete 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.

The Cheeger constant of curved strips

PRATELLI, ALDO
2011-01-01

Abstract

We study the Cheeger constant and Cheeger set for domains obtained as strip-like neighborhoods 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 noncomplete 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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11571/275703
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