All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Page 1

Displaying 1 – 14 of 14

Showing per page

Shift inequalities of Gaussian type and norms of barycentres

F. Barthe, D. Cordero-Erausquin, M. Fradelizi (2001)

Studia Mathematica

We derive the equivalence of different forms of Gaussian type shift inequalities. This completes previous results by Bobkov. Our argument strongly relies on the Gaussian model for which we give a geometric approach in terms of norms of barycentres. Similar inequalities hold in the discrete setting; they improve the known results on the so-called isodiametral problem for the discrete cube. The study of norms of barycentres for subsets of convex bodies completes the exposition.

Singular integrals and rectifiability.

Pertti Mattila (2002)

Publicacions Matemàtiques

We shall discuss singular integrals on lower dimensional subsets of Rn. A survey of this topic was given in [M4]. The first part of this paper gives a quick review of some results discussed in [M4] and a survey of some newer results and open problems. In the second part we prove some results on the Riesz kernels in Rn. As far as I know, they have not been explicitly stated and proved, but they are very closely related to some earlier results and methods.[Proceedings of the 6th International Conference...

Solution to the gradient problem of C.E. Weil.

Zoltán Buczolich (2005)

Revista Matemática Iberoamericana

In this paper we give a complete answer to the famous gradient problem of C. E. Weil. On an open set G ⊂ R2 we construct a differentiable function f: G → R for which there exists an open set Ω1 ⊂ R2 such that ∇f(p) ∈ Ω1 for a p ∈ G but ∇f(q) ∉ Ω1 for almost every q ∈ G. This shows that the Denjoy-Clarkson property does not hold in higher dimensions.

Sous-ensembles de courbes Ahlfors-régulières et nombres de Jones.

Hervé Pajot (1996)

Publicacions Matemàtiques

We prove that an Ahlfors-regular set (with dimension one) E ⊂ Rn which verifies a βq-version of P. W. Jones' geometric lemma is included in an Ahlfors-regular curve Γ.This theorem is due to G. David and S. Semmes, we give a more direct proof.

Spaces of σ-finite linear measure

Ihor Stasyuk, Edward D. Tymchatyn (2013)

Colloquium Mathematicae

Spaces of finite n-dimensional Hausdorff measure are an important generalization of n-dimensional polyhedra. Continua of finite linear measure (also called continua of finite length) were first characterized by Eilenberg in 1938. It is well-known that the property of having finite linear measure is not preserved under finite unions of closed sets. Mauldin proved that if X is a compact metric space which is the union of finitely many closed sets each of which admits a σ-finite linear measure then...

Currently displaying 1 – 14 of 14

Page 1