Cn Functions, Hausdorff Measures, and Analytic Sets

Hausdorff-analytic Functions of Matrices1

Hausdorff Dimension and Hausdorff Measures of Julia Sets of Elliptic Functions

Hausdorff Dimension and Conformal Measures of Feigenbaum Julia Sets

1.1. Statement of the results. One of the first questions usually asked about a fractal subset of R is whether it has the maximal possible Hausdorff dimension, n. It certainly happens if the set has positive Lebesgue measure. On the other hand, it is easy to construct fractal sets of zero measure but of dimension n. Moreover, this phenomenon is often observable for fractal sets produced by conf...

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 γ : R → R , N ≥ 2, is locally 1-monotone.

Numerical analytic continuation of holomorphic functions in Cn