CHARACTERIZATION OF CHEEGER SETS FOR CONVEX SUBSETS OF THE PLANE

By B. Kawohl, Thomas Lachand-Robert. 2006

147 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/3ddb488258a28c93a9886d7ed4b7425a07cef90e

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

An overview on the Cheeger problem (2015, background): “We now focus on the Cheeger problem, and in doing so we first present some general properties of the Cheeger constant h(Ω) and of Cheeger sets inside Ω, valid for any dimension n ≥ 2 (see [34, 22, 23]).”
Overdetermined problems with possibly degenerate ellipticity, a geometric approach (2006, background): “According to [24] and [25] we say that Ω coincides with its Cheeger set if |∂Ω| |Ω| = min D |∂D| |D| := h(Ω)”
On the Cheeger sets in strips and non-convex domains (2014, background): “5 (taken from [16]), or were all contained into each other, as for instance in Example 4.”
An introduction to Total Variation for Image Analysis (2009, background): “An accurate study (see also [5, 4, 42]) shows that, if we define (for C = [0, 1]2) CR = ⋃”
Uniqueness of the Cheeger set of a convex body (2007, background): “In that case, the Cheeger set of is unique and equals the set R ⊕ B(0, R), where R := {x ∈ : dist(x, ∂ ) > R} is such that | R| = π R2 and A ⊕ B := {a + b : a ∈ A, b ∈ B}, for A, B ⊂ R2 [Alter et al. 2005b; Kawohl and Lachand-Robert 2006].”
A characterization of convex calibrable sets in RN with respect to anisotropic norms (2008, background): “This has been proved in [27,14,30] (see also [3]) though it was stated in terms of calibrability in [14,3].”
On a weighted total variation minimization problem (2007, background): “Problem (4) is famous and known as Cheeger’s problem [3], its value λ(Ω) is called the Cheeger constant of Ω and its minimizers are called Cheeger sets of Ω (see [9], [10] and the references therein).”
Very singular diffusion equations: second and fourth order problems (2010, background): “Flat portion such that the speed is constant is called a calibrable set for E or a Cheeger set studied by people including Kawohl and co-author [ 76 ,77].”
AN INTRODUCTION TO THE CHEEGER PROBLEM (2011, background): “If Ω is not convex, one can not expect in general uniqueness of the Cheeger set, as shown by simple examples such as the ”barbell domain” (see [19]).”