Regularity of push-forward of Monge-Amp{\`e}re measures

TL;DR

This paper demonstrates that the push-forward of Monge-Ampère measures of Hölder continuous quasi-psh functions retains a Hölder potential under dominant meromorphic maps, extending to lower regularity cases.

Contribution

It establishes the regularity preservation of Monge-Ampère measures under meromorphic maps, a novel result in complex pluripotential theory.

Findings

Push-forward measures have Hölder potentials

Results extend to functions with lower regularity

Provides new insights into measure regularity under meromorphic maps

Abstract

We prove that the image under any dominant meromorphic map of the Monge-Amp{\`e}re measure of a H{\"o}lder continuous quasi-psh function still possesses a H{\"o}lder potential. We also discuss the case of lower regularity.