Displaying similar documents to “A covering property of some classes of sets in ℝ 2 ”

Covering lemmas and BMO estimates for eigenfunctions on Riemannian surfaces.

Guozhen Lu (1991)

Revista Matemática Iberoamericana

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The principal aim of this note is to prove a covering Lemma in R. As an application of this covering lemma, we can prove the BMO estimates for eigenfunctions on two-dimensional Riemannian manifolds (M, g). We will get the upper bound estimate for || log |u| ||, where u is the solution to Δu + λu = 0, for λ > 1 and Δ is the Laplacian on (M, g). A covering lemma on homogeneous spaces is also obtained in this note.

On a generalization of the Selection Theorem of Mahler

Gilbert Muraz, Jean-Louis Verger-Gaugry (2005)

Journal de Théorie des Nombres de Bordeaux

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The set 𝒰 𝒟 r of point sets of ℝ n , n ≥ 1 , having the property that their minimal interpoint distance is greater than a given strictly positive constant r > 0 is shown to be equippable by a metric for which it is a compact topological space and such that the Hausdorff metric on the subset 𝒰 𝒟 r , f ⊂ 𝒰 𝒟 r of the finite point sets is compatible with the restriction of this topology to 𝒰 𝒟 r , f . We show that its subsets of Delone sets of given constants in ℝ n , n ≥ 1 , are compact. Three (classes of) metrics, whose one of crystallographic...