Corollary 18.18.515AC4263456B

Corollary 18.18.5.15AC4263456B For each $i$, let $\sigma _{i,j}$ be smooth real forms on $C_ i$ of nonnegative area that converge uniformly, as $j\to \infty $, to a smooth form $\sigma _{i,0}$ of area zero, and write $\sigma _ j=(\sigma _{1,j},\ldots ,\sigma _{m,j})$. For any nonnegative smooth auxiliary coefficients $f_ j$, the diameters of $\mathcal S_{\sigma _ j}$ tend to zero. For every fixed smooth positive volume form on $M$, the potentials in $\mathcal S_{\sigma _ j}$ converge in $L^1(M)$ to

uniformly over all normalized model tuples.