Work

On Kähler-Einstein Currents

Year: 2025

Type: preprint

Abstract: We show that a general class of singular Kähler metrics with Ricci curvature bounded below define Kähler currents. In particular the result applies to singular Kähler-Einstein metrics on klt pairs, and an analogous result holds for Kähler-Ricci solitons. In addition we show that if a singular Kähler-Einstein metric can be approximated by smooth metrics on a resolution whose Ricci curvature has negative part that is bounded uniformly in $L^p$ for $p > \frac{2n-1}{n}$, then the metric defines an RCD space.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2502.09825

Authors: Chen, Yifan, Chiu, Shih-Kai, Hallgren, Max, Székelyhidi, Gábor, Tô, Tat Dat, Tong, Freid

Institutions: Rutgers, The State University of New Jersey, South China University of Technology, University of California, Berkeley, Institut de Mathématiques de Jussieu-Paris Rive Gauche, Sorbonne Université, Université Paris Diderot

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4407632311

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