Codimension four regularity of generalized Einstein structures

TL;DR

This paper proves that sequences of generalized Einstein metrics with bounded Ricci-like tensors are regular outside a set of codimension four, providing curvature estimates, finiteness, and rigidity results.

Contribution

It establishes codimension four regularity for generalized Einstein structures with bounds on natural Ricci generalizations, including curvature estimates and finiteness theorems.

Findings

Codimension four regularity of generalized Einstein structures.

A priori L2 curvature estimates for these spaces.

Diffeomorphism finiteness and rigidity results.

Abstract

We establish codimension 4 regularity of noncollapsed sequences of metrics with bounds on natural generalizations of the Ricci tensor. We obtain a priori L2 curvature estimates on such spaces, with diffeomorphism finiteness results and rigidity theorems as corollaries.