A complete metric topology on relative low energy spaces

TL;DR

This paper establishes a natural, completely metrizable topology on low energy spaces in the context of prescribed singularities, which extends beyond convergence in capacity.

Contribution

It introduces a new, natural metric topology on low energy spaces in complex geometry, enhancing understanding of their structure.

Findings

The topology on low energy spaces is completely metrizable.

This topology is stronger than convergence in capacity.

Provides a framework for analyzing singularity-prescribed spaces.

Abstract

In this paper, we show that the low energy spaces in the prescribed singularity case $\mathcal{E}_{\psi}(X,\theta,\phi)$ have a natural topology which is completely metrizable. This topology is stronger than convergence in capacity.