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arXiv · 2310.08647

Singular sets on spaces with integral curvature bounds and diffeomorphism finiteness for manifolds

Xin Qian
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Abstract

In this paper, we are concerned with noncollapsed Riemannian manifolds $(M^{n},g)$ with integral curvature bounds, as well as their Gromov-Hausdorff limits $(M^{n}_{i},g_{i})\xrightarrow{GH}(X,d)$. Our main result generalizes Cheeger's Hausdorff dimension estimate for the singular set in [7] and improve it into Minkowski dimension estimate in the spirit of Cheeger-Naber [12]. We also prove a difffeomorphism finiteness theorem for manifolds in the critical case, using Cheeger-Naber's methods in [13].

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Xin Qian. 2023-10-12. Singular sets on spaces with integral curvature bounds and diffeomorphism finiteness for manifolds. https://doi.org/10.1007/s00526-024-02869-4

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