Definition 17.7.1B0604A42ABDF

Definition 17.7.1.B0604A42ABDF Let $u_0,u_1\in \mathrm{PSH}(X,\theta )$. A subgeodesic with endpoints $u_0,u_1$ is a family $(u_ t)_{0<t<1}$ of functions on $X$ whose complexification

is $p^*\theta $-psh on $X\times S$ and such that $u_ t\to u_0$ and $u_ t\to u_1$ in $L^1(X)$ as $t\to 0$ and $t\to 1$, respectively.