Addition linearer Cantormengen
Almost sure asymptotic behaviour of the -neighbourhood surface area of Brownian paths
We show that whenever the -dimensional Minkowski content of a subset exists and is finite and positive, then the “S-content” defined analogously as the Minkowski content, but with volume replaced by surface area, exists as well and equals the Minkowski content. As a corollary, we obtain the almost sure asymptotic behaviour of the surface area of the Wiener sausage in , .
An alternative concept of the n-dimensional measure
An analog of Sard's theorem for -smooth functions of two variables.
An area formula in metric spaces
We present an area formula for continuous mappings between metric spaces, under minimal regularity assumptions. In particular, we do not require any notion of differentiability. This is a consequence of a measure-theoretic notion of Jacobian, defined as the density of a suitable "pull-back measure". Finally, we give some applications and examples.
An Equipartition of Planar Sets.
An semigroup of zero measure which contains a translate of every countable set
An isoperimetric inequality in R3
An isoperimetric inequality on the ℓp balls
The normalised volume measure on the ℓnp unit ball (1≤p≤2) satisfies the following isoperimetric inequality: the boundary measure of a set of measure a is at least cn1/pãlog1−1/p(1/ã), where ã=min(a, 1−a).
Analytic capacity and linear measure
Approximate isometries on bounded sets with an application to measure theory
Asymptotic distribution of coordinates on high dimensional spheres.
Au bord de certains polyèdres hyperboliques
Le cadre de cet article est celui des groupes et des espaces hyperboliques de M. Gromov. Il est motivé par la question suivante : comment différencier deux groupes hyperboliques à quasi-isométrie près ? On illustre ce problème en détaillant un exemple de M. Gromov issu de Asymptotic invariants for infinite groups. On décrit une famille infinie de groupes hyperboliques, deux à deux non quasi-isométriques, de bord la courbe de Menger. La méthode consiste à étudier leur structure quasi-conforme au...
spaces and rectifiability for Carnot-Carathéodory metrics: an introduction
This paper is meant as a (short and partial) introduction to the study of the geometry of Carnot groups and, more generally, of Carnot-Carathéodory spaces associated with a family of Lipschitz continuous vector fields. My personal interest in this field goes back to a series of joint papers with E. Lanconelli, where this notion was exploited for the study of pointwise regularity of weak solutions to degenerate elliptic partial differential equations. As stated in the title, here we are mainly concerned...
Berichtigung zu der Arbeit "Diskrepanz und Distanz von Maßen bezüglich konvexer und Jordanscher Mengen". Math. Z. 144, 125 - 134 (1975).
Besicovitch via Baire
We construct various Besicovitch sets using Baire category arguments.
Besicovitch's circle pairs, analytic capacity, and Cauchy integrals for a class of unrectifiable 1-sets.
Besicovitch-type properties of measures and submanifolds.
Best constants for the isoperimetric inequality in quantitative form
We prove some results in the context of isoperimetric inequalities with quantitative terms. In the -dimensional case, our main contribution is a method for determining the optimal coefficients in the inequality , valid for each Borel set with positive and finite area, with and being, respectively, the and the of . In dimensions, besides proving existence and regularity properties of minimizers for a wide class of including the lower semicontinuous extension of , we describe the...
Bi-Lipschitz decomposition of Lipschitz functions into a metric space.