Type problem, the first eigenvalue and Hardy inequalities

Gilles Carron, Bo-Yong Chen, Yuanpu Xiong

In this paper, we study the relationship between the type problem and the asymptotic behaviour of the first (Dirichlet) eigenvalues ${\lambda }_1(B_r)$ of ``balls'' $B_r:=\{\rho <r\}$ on a comp…