PomeDefinition 5.40.4.65C9C3635D58 For $u\in \mathrm{PSH}(X,\theta )$, set
\[ P_\theta [u] =\left(\lim _{C\to +\infty }P_\theta (u+C,0)\right)^* =\left(\sup \{ h\in \mathrm{PSH}(X,\theta ):h\preceq u,\ h\leq 0\} \right)^*. \]
We call $u$ an envelope fixed point, or an ordinary model, if $P_\theta [u]=u$; in the Kähler literature such potentials are called model potentials. For $F\in C^\infty (X,\mathbb R)$, replacing the constraint $h\leq 0$ by $h\leq F$ defines $P_{\theta ,F}[u]$.
Comments
Corrections, questions, and mathematical discussion are welcome. Sign in with GitHub to comment. Comments are public.