# The K\"ahler Ricci flow around complete bounded curvature K\"ahler metrics

## TL;DR

This paper develops existence and stability results for the Kähler Ricci flow on complete manifolds with bounded curvature, including non-smooth and degenerate initial conditions, advancing understanding of geometric evolution in complex geometry.

## Contribution

It introduces new existence time estimates for the Kähler Ricci flow starting from various initial conditions, including non-smooth and degenerate metrics.

## Key findings

- Established existence of solutions with bounded curvature under minimal initial assumptions
- Derived stability results for complex space forms under the flow
- Extended flow results to non-smooth and degenerate initial data

## Abstract

We produce complete bounded curvature solutions to K\"ahler-Ricci flow with existence time estimates, assuming only that the initial data is a smooth \K metric uniformly equivalent to another complete bounded curvature \K metric. We obtain related flow results for non-smooth as well as degenerate initial conditions. We also obtain a stability result for complex space forms under the flow.