Packing dimension and Ahlfors regularity of porous sets in metric spaces

Esa Järvenpää, Maarit Järvenpää, Antti Käenmäki +3

Let $X$ be a metric measure space with an $s$-regular measure $\mu$. We prove that if $A\subset X$ is $\varrho$-porous, then ${\dim }_{\mathrm{p}}(A)\le s-c{\varrho }^s$ where $\dim_{\math…