Complex analysis siu

In complex analysis, the Siu semicontinuity theorem implies that the Lelong number of a closed positive current on a complex manifold is semicontinuous.
More precisely, the points where the Lelong number is at least some constant form a complex subvariety.
This was conjectured by Harvey & King (1972) and proved by Siu.
Demailly (1987) generalized Siu's theorem to more general versions of the Lelong number.

Yum-Tong Siu is the William Elwood Byerly Professor of Mathematics at Harvard University.