Long Li, Plurisubharmonic functions and Sasaki geometry

In this talk, we will discuss the recent progress on the zero mass conjecture for plurisubharmoinc functions, raised by Guedj and Rashkovskii. For a local plurisubharmonic function with an isolated singularity at the origin, the conjecture states that the zero Lelong number (at the singularity) implies the zero residual Monge-Ampere mass at the same point. We confirm this conjecture under the circular symmetry condition, with the aid from Sasaki geometry. Furthermore, we will also apply our technique to more general plurisubharmonic functions in certain cases.