Regularity of the equilibrium measure for meromorphic correspondences

TL;DR

This paper investigates the regularity properties of the equilibrium measure associated with a meromorphic correspondence on a compact Kähler manifold, under specific degree conditions, using super-potentials.

Contribution

It provides a quantitative regularity result for the equilibrium measure of meromorphic correspondences based on super-potentials, under certain degree assumptions.

Findings

Established regularity estimates for the equilibrium measure.

Linked the measure's regularity to the super-potentials of the correspondence.

Demonstrated the impact of degree conditions on measure regularity.

Abstract

Let $f$ be a meromorphic correspondence on a compact K\"ahler manifold $X$ of dimension $k$. Assume that its topological degree is larger than the dynamical degree of order $k-1$. We obtain a quantitative regularity of the equilibrium measure of $f$ in terms of its super-potentials.