Resolution of compact Einstein orbifolds in general dimensions
Differential Geometry
2026-03-17 v1
Abstract
Given a noncollapsing sequence of m-dimensional compact Einstein manifolds with a uniform energy bound, the Gromov-Hausdorff limit is a compact Einstein orbifold with at most finitely many singularities. Conversely, starting with a compact Einstein orbifold, we are interested in whether there exists a sequence of smooth Einstein metrics converging to it. In this paper, we provide a negative answer. We give an explicit obstruction for a negative Einstein orbifold appearing as a noncollapsing limit of compact Einstein manifolds, which does not vanish for hyperbolic orbifolds. This work extends the work of Ozuch in dimension 4, with significant technical simplifications.
Cite
@article{arxiv.2603.14929,
title = {Resolution of compact Einstein orbifolds in general dimensions},
author = {Yichen Yao},
journal= {arXiv preprint arXiv:2603.14929},
year = {2026}
}