# Donaldson's $Q$-operators for symplectic manifolds

## TL;DR

This paper establishes an estimate for Donaldson's $Q$-operator on compact symplectic manifolds, contributing to a symplectic analogue of scalar curvature bounds relevant in geometric analysis.

## Contribution

It provides a key estimate for Donaldson's $Q$-operator, advancing the understanding of scalar curvature bounds in symplectic geometry.

## Key findings

- Derived a new estimate for Donaldson's $Q$-operator
- Supported a symplectic generalization of scalar curvature bounds
- Contributed to the proof of a lower bound for Hermitian scalar curvature

## Abstract

We prove an estimate for Donaldson's $Q$-operator on a prequantized compact symplectic manifold. This estimate is an ingredient in the recent result of Keller and Lejmi about a symplectic generalization of Donaldson's lower bound for the $L^2$-norm of the Hermitian scalar curvature.