# Locally Removable Singularities for K\"{a}hler Metrics with Constant Holomorphic Sectional Curvature

## TL;DR

This paper proves that Kähler metrics with constant holomorphic sectional curvature on punctured unit balls in complex space can be uniquely extended over certain compact singular sets, using developing map theory.

## Contribution

It establishes a new extension result for Kähler metrics with constant holomorphic sectional curvature over specific singularities in complex balls.

## Key findings

- Kähler metrics extend uniquely over certain compact singular sets.
- Developing map theory is used to prove the extension.
- Extension holds for both general compact sets and specific linear subspaces.

## Abstract

Let $n\ge 2$ be an integer, and $B^{n}\subset \mathbb{C}^{n}$ the unit ball. Let $K\subset B^{n}$ be a compact subset such that $B^n\setminus K$ is connected, or $K=\{z=(z_1,\cdots, z_n)|z_1=z_2=0\}\subset \mathbb{C}^{n}$. By the theory of developing maps, we prove that a K\"{a}hler metric on $B^{n}\setminus K$ with constant holomorphic sectional curvature uniquely extends to $B^{n}$.