Compactness of K\"ahler metrics with bounds on Ricci curvature and I functional

TL;DR

This paper establishes a compactness theorem for K"ahler metrics under bounds on Ricci curvature and the I functional, with applications to the continuity method and Calabi flow.

Contribution

It introduces a new compactness result for K"ahler metrics with specific curvature and functional bounds, advancing understanding in geometric analysis.

Findings

Proved a compactness theorem for K"ahler metrics.

Applied the theorem to the continuity method.

Applied the theorem to the Calabi flow.

Abstract

We prove a compactness theorem for K\"ahler metrics with various bounds on Ricci curvature and the $\mathcal I$ functional. We explore applications of our result to the continuity method and the Calabi flow.