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arXiv · 2604.26399

Gromov-Hausdorff limit of orthonormal frame bundles of non-collapsed manifolds with bounded Ricci curvature

Cuifang Si·Shicheng Xu
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Abstract

Let $M_i$ be a sequence of non-collapsed $n$-manifolds with two-sidedly bounded Ricci curvature. We show that the Gromov-Haudorff limit space, $Y$, of the associated sequence of orthonormal frame bundles, $FM_i$, equipped with an almost canonical metric, shares similar properties as a Ricci limit space of non-collapsing sequence i.e., the singular set has codimension $\ge 4$ whose complement contains an open and dense $C^{1,\alpha}$-Riemannian manifold.

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Cuifang Si, Shicheng Xu. 2026-04-29. Gromov-Hausdorff limit of orthonormal frame bundles of non-collapsed manifolds with bounded Ricci curvature. https://doi.org/10.1142/s0219199726500495

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