# The continuity equation with cusp singularities

## TL;DR

This paper investigates the behavior of cusp Kähler-Einstein metrics during the continuity process, focusing on their geometric and algebraic properties near singularities and limits.

## Contribution

It introduces a detailed study of cusp singularities in the context of the continuity method for Kähler-Einstein metrics, expanding understanding of their limits and properties.

## Key findings

- Analysis of noncollapsing limits with cusp singularities
- Characterization of geometric properties near cusp singularities
- Insights into the algebro-geometric structure of the limits

## Abstract

In this paper we study a special case of the completion of cusp K\"{a}hler-Einstein metric on the regular part of varieties by taking the continuity method proposed by La Nave and Tian. The differential geometric and algebro-geometric properties of the noncollapsing limit in the continuity method with cusp singularities will be investigated.