On the residual Monge-Amp\`{e}re mass of plurisubharmonic functions with symmetry, II

TL;DR

This paper investigates the residual Monge-Ampère mass of circularly symmetric plurisubharmonic functions with isolated singularities, providing estimates that relate to their Lelong numbers and addressing a conjecture in complex geometry.

Contribution

It introduces new estimates on the residual Monge-Ampère mass using Sasakian geometry, advancing understanding of the zero mass conjecture for symmetric functions.

Findings

Derived bounds on residual mass in terms of Lelong numbers

Partially confirmed the zero mass conjecture for symmetric cases

Connected geometric structures with complex analysis properties

Abstract

The aim of this article is to study the residual Monge-Amp\`{e}re mass of a plurisubharmonic function with an isolated singularity, provided with the circular symmetry. With the aid of Sasakian geometry, we obtain an estimate on the residual mass of this function with respect to its Lelong number and maximal directional Lelong number. This result partially answers the zero mass conjecture raised by Guedj and Rashkovskii.