Generalized mean porosity and dimension.
Geometric Properties of Minimal Surfaces with Free Boundaries.
Gradual doubling property of Hutchinson orbits
The classical self-similar fractals can be obtained as fixed points of the iteration technique introduced by Hutchinson. The well known results of Mosco show that typically the limit fractal equipped with the invariant measure is a (normal) space of homogeneous type. But the doubling property along this iteration is generally not preserved even when the starting point, and of course the limit point, both have the doubling property. We prove that the elements of Hutchinson orbits possess the doubling...
Graphen reeller Funktionen.
Groupes engendrés par des ensembles compacts Lebesgue-négligeables
Harmonic, Gibbs and Hausdorff measures on repellers for holomorphic maps, II
Harmonic measures versus quasiconformal measures for hyperbolic groups
We establish a dimension formula for the harmonic measure of a finitely supported and symmetric random walk on a hyperbolic group. We also characterize random walks for which this dimension is maximal. Our approach is based on the Green metric, a metric which provides a geometric point of view on random walks and, in particular, which allows us to interpret harmonic measures as quasiconformal measures on the boundary of the group.
Hausdorff dimension of uniformly non flat sets with topology.
Hausdorff measures in Minkowskian geometry
Hausdorff measures of the set of critical values of functions of the class
Hausdorff-Maße von Summenmengen. I.
Hausdorff-Maße von Summenmengen. II:
Heisenberg Hausdorff Dimension of Besicovitch Sets
We consider (bounded) Besicovitch sets in the Heisenberg group and prove that Lp estimates for the Kakeya maximal function imply lower bounds for their Heisenberg Hausdorff dimension.
Hrášek a sluníčko. O matematickém paradoxu Stefana Banacha a Alfreda Tarského
Inégalités isopérimétriques en analyse et probabilités
-distance sets, Falconer conjecture, and discrete analogs.
Local Lyapunov exponents and a local estimate of Hausdorff dimension
Local monotonicity of Hausdorff measures restricted to curves in
We give a sufficient condition for a curve to ensure that the -dimensional Hausdorff measure restricted to is locally monotone.
Local monotonicity of Hausdorff measures restricted to real analytic curves
We prove that the 1-dimensional Hausdorff measure restricted to a simple real analytic curve , , is locally 1-monotone.
Local monotonicity of measures supported by graphs of convex functions.