Estimates for metrics of constant Chern scalar curvature

TL;DR

This paper extends recent results by Chen-Cheng to establish a priori estimates for metrics with constant Chern scalar curvature on compact complex manifolds, contingent on an entropy upper bound.

Contribution

It generalizes Chen-Cheng's Kähler results to the broader setting of complex manifolds with Chern scalar curvature.

Findings

Established a priori estimates under entropy bounds

Extended Kähler results to complex manifolds

Provided new bounds for Chern scalar curvature metrics

Abstract

We prove a priori estimates for constant Chern scalar curvature metrics on a compact complex manifold conditional on an upper bound on the entropy, extending a recent result by Chen-Cheng in the K\"ahler setting.