A counterexample to the zero-mass conjecture
arXiv:2607.26549
summary
The authors construct an explicit negative plurisubharmonic function on the unit polydisk whose Monge‑Ampère measure is a Dirac mass at the origin while its Lelong number is zero, providing a counterexample to the zero‑mass conjecture in all complex dimensions ≥2.
Abstract
We construct an explicit negative plurisubharmonic function on the unit polydisk in with an isolated singularity at the origin. Its Monge-Ampère measure is the Dirac mass at the origin, but its Lelong number vanishes. This gives a negative answer to the zero-mass conjecture of Guedj-Rashkovskii in every complex dimension at least two.
Topics & keywords
#plurisubharmonic functions#monge-ampere measure#zero-mass conjecture#lelong number#counterexampleplurisubharmonicMonge‑Ampère operatorDirac massLelong numberunit polydisk