A scalar curvature bound along the conical K\"ahler-Ricci flow

TL;DR

This paper establishes a uniform scalar curvature bound for solutions to the conical K"ahler-Ricci flow starting from a model conical metric, under certain semi-ampleness conditions, and provides uniform estimates for potentials and derivatives.

Contribution

It introduces a scalar curvature bound for the conical K"ahler-Ricci flow under semi-ampleness assumptions, extending previous results to conical settings.

Findings

Proves a uniform scalar curvature bound for the flow.

Establishes uniform estimates for potentials and their derivatives.

Extends scalar curvature bounds to conical K"ahler-Ricci flows.

Abstract

Starting with a model conical K\"ahler metric, we prove a uniform scalar curvature bound for solutions to the conical K\"ahler-Ricci flow assuming a semi-ampleness type condition on the twisted canonical bundle. In the proof, we also establish uniform estimates for the potentials and their time derivatives.