Singular sets on spaces with integral curvature bounds and diffeomorphism finiteness for manifolds
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866912170864803840 |
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| author | Qian, Xin |
| author_facet | Qian, Xin |
| contents | 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]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_08647 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Singular sets on spaces with integral curvature bounds and diffeomorphism finiteness for manifolds Qian, Xin Differential Geometry Metric Geometry 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]. |
| title | Singular sets on spaces with integral curvature bounds and diffeomorphism finiteness for manifolds |
| topic | Differential Geometry Metric Geometry |
| url | https://arxiv.org/abs/2310.08647 |