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An algorithm for computing the centered Hausdorff measure of self-similar sets
centered Hausdorff measure self-similar sets computability of fractal measures
2011/9/15
Abstract: We provide an algorithm for computing the centered Hausdorff measure of self-similar sets satisfying the strong separation condition. We prove the convergence of the algorithm and test its u...
Singular integrals on self-similar sets and removability for Lipschitz harmonic functions in Heisenberg groups
Singular integrals self-similar sets removability Heisenberg group
2011/1/20
In this paper we study singular integrals on small (that is, measure zero and lower than full dimensional) subsets of metric groups. The main examples of the groups we have in mind are Euclidean space...
Nontangential limits and Fatou-type theorems on post-critically finite self-similar sets
Fatou-type theorems post-critically finite self-similar sets
2010/11/18
In this paper we study the boundary limit properties of harmonic functions on $\mathbb R_+\times K$, the solutions $u(t,x)$ to the Poisson equation \[ \frac{\partial^2 u}{\partial t^2} + \Delta u = 0...
For a large class of self-similar sets F in Rd, analogues of the higher order mean curvatures
of differentiable submanifolds are introduced, in particular, the fractal Gauss-type curvature.
They are...