198 citations · 1.1k across the 43 of their papers we have counts for
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Self-Similar Topological Fractals
Fabio E. G. Cipriani, Daniele Guido, Tommaso Isola +1
We introduce the notion of (abelian) similarity scheme, as a constructive model for topological self-similar fractals, in the same way in which the notion of iterated function syst…
Integrals and Potentials of Differential 1-forms on the Sierpinski Gasket
Fabio Cipriani, Daniele Guido, Tommaso Isola +1
We provide a definition of integral, along paths in the Sierpinski gasket K, for differential smooth 1-forms associated to the standard Dirichlet form K. We show how this tool can…
Tangential dimensions II. Measures
Daniele Guido, Tommaso Isola
Notions of (pointwise) tangential dimension are considered, for measures of R^n. Under regularity conditions (volume doubling), the upper resp. lower dimension at a point x of a me…
Tangential dimensions I. Metric spaces
Daniele Guido, Tommaso Isola
Pointwise tangential dimensions are introduced for metric spaces. Under regularity conditions, the upper, resp. lower, tangential dimensions of X at x can be defined as the supremu…