A new metric d_S on singularity types of θ-psh potentials is defined; on positive-mass classes it is complete, and it governs convergence of solutions and multiplier ideal sheaves.
Berndtsson, The openness conjecture and complex Brunn-Minkowski inequalities, Complex geometry and dynamics, 29--44, Abel Symp., 10, Springer, Cham, 2015
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The metric geometry of singularity types
A new metric d_S on singularity types of θ-psh potentials is defined; on positive-mass classes it is complete, and it governs convergence of solutions and multiplier ideal sheaves.