$\tau$-tilting finiteness of two-point algebras II

In this paper, we explain a strategy on $g$-vectors to discover some new minimal $\tau$-tilting infinite two-point algebras. Consequently, the $\tau$-tilting finiteness of various two-point monomial algebras, including all radical cube zero cases, could be determined. Moreover, we find that the derived equivalence class of the Kronecker algebra contains only itself and its opposite algebra.