Continuous L2-optimal Hermitian metrics satisfy an optimal L2 extension inequality with the logarithmic capacity constant, which implies they are Griffiths semi-positive.
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An optimal $L^2$ extension for continuous $L^2$-optimal Hermitian metrics
Continuous L2-optimal Hermitian metrics satisfy an optimal L2 extension inequality with the logarithmic capacity constant, which implies they are Griffiths semi-positive.