**abstract:**
I will discuss the relationship between Hardy's inequality, a pointwise Hardy inequality, a uniform capacity density condition and a boundary Poincaré inequality in doubling metric spaces supporting a Poincaré inequality. All of these conditions can be used to describe the size of the boundary of a set. In particular, I will concentrate in explaining the main ideas behind the proof of the equivalence of the three conditions. The talk is based on joint work with Juha Lehrbäck and Heli Tuominen.

Thu 13 Jan, 16:50 - 17:20, Aula Dini

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