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arXiv · 2602.04569

Bi-Lipschitz Smoothing under Ricci and Injectivity Bounds

Maja Gwozdz
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Abstract

We prove that a complete Riemannian manifold with a positive uniform lower bound on injectivity radius and a positive uniform lower bound on Ricci curvature admits an $L^\infty$-close (bi-Lipschitz) smooth metric with two-sided Ricci curvature bounds and a uniform positive lower bound on injectivity radius. This answers Question 2 in the Morgan--Pansu list of open problems from the conference Modern Trends in Differential Geometry (S\~ao Paulo, 2018), proposed by L. Bandara. In the proof, we rely on controlled smoothing with Croke's universal local volume lower bound and the Cheeger--Gromov--Taylor injectivity radius estimate.

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Maja Gwozdz. 2026-02-04. Bi-Lipschitz Smoothing under Ricci and Injectivity Bounds. https://arxiv.org/abs/2602.04569

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