On upper conical density results

Abstract

We report a recent developement on the theory of upper conical densities. More precicely, we look at what can be said in this respect for other measures than just the Hausdorff measure. We illustrate the methods involved by proving a result for the packing measure and for a purely unrectifiable doubling measure.

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References in corpus (5)

• Packing dimension and Ahlfors regularity of porous sets in metric spaces
• Conical upper density theorems and porosity of measures
• Nonsymmetric conical upper density and $k$-porosity
• Directed porosity on conformal iterated function systems and weak convergence of singular integrals
• Upper Conical density results for general measures on ${\mathbb{R}}^n$

Cited by in corpus (1)

• Scenery flow, conical densities, and rectifiability