Local curvature estimates along the $\kappa$-LYZ flow

TL;DR

This paper establishes local curvature estimates for the $ abla$-LYZ flow on Kähler manifolds, enabling the extension of the flow's existence over longer periods and broadening understanding of its geometric behavior.

Contribution

It provides the first local curvature estimate for the $ abla$-LYZ flow, generalizing previous results on long-term existence of the flow.

Findings

Proved local curvature bounds for the $ abla$-LYZ flow.

Extended the known long-time existence results for the flow.

Enhanced understanding of the flow's behavior on Kähler manifolds.

Abstract

In this paper we prove a local curvature estimate for the $\kappa$-LYZ flow over K\"ahler manifolds introduced in [FGP1] and [LYZ]. In particular, we generalize the long time existence of the flow.