Jun Kigami: Ahlfors regular conformal dimension and critical value of p-energies of a compact metric space

Given a metric space, we are going to identify Ahlfors regular conformal dimension with the critical value of p-energies associated with the canonical partition of the metric space. Such an identification has been shown by M. Carassco Piaggio for the case of the critical index for discrete modulus. Moreover, we are going to show a relation between the Ahlfors regular conformal dimension and the spectral dimension.