Definition 17.17.2.7D4FF1072CEF An envelope test curve with initial potential $\varphi $ consists of a real number $c$ and potentials $\Gamma _\tau \in \mathrm{PSH}(X,\theta )$ for $\tau <c$ such that
$\tau \mapsto \Gamma _\tau $ is pointwise concave and decreasing;
$P_\theta [\Gamma _\tau ]=\Gamma _\tau $ for every $\tau <c$;
$(\sup _{\tau <c}\Gamma _\tau )^*=\varphi $.
Its cutoff is $c$. We extend it by
\[ \Gamma _ c=\lim _{\tau \uparrow c}\Gamma _\tau , \qquad \Gamma _\tau \equiv -\infty \quad (\tau >c). \]
Comments
Corrections, questions, and mathematical discussion are welcome. Sign in with GitHub to comment. Comments are public.