Integral bounds on curvature and Gromov-Hausdorff limits

TL;DR

This paper introduces a novel approach to bounding curvature integrals on Riemannian manifolds near singularities, extending prior results on Gromov-Hausdorff limits and curvature norms.

Contribution

It provides new integral bounds on curvature for manifolds close to singular spaces, extending Cheeger, Colding, and Tian's work with small extensions.

Findings

Established bounds on the $L^{k/2}$ norm of curvature near singularities

Extended previous results on Gromov-Hausdorff limits and curvature estimates

Improved understanding of curvature behavior near codimension $k$ singularities

Abstract

We develop a new approach to, and small extension of, results of Cheeger, Colding and Tian concerning the $L^{k/2}$ norm of the curvature of a Riemannian manifold Gromov-Hausdorff close to a codimension $k$ singularity.