Strong Kato limit can be branching
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909942173138944 |
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| author | Carron, Gilles Mondello, Ilaria Tewodrose, David |
| author_facet | Carron, Gilles Mondello, Ilaria Tewodrose, David |
| contents | We provide an example of a non-collapsed strong Kato limit that is branching, essentially branching, and satisfies neither the $\mathrm{CD}(K,\infty)$ nor the $\mathrm{MCP}(K,N)$ conditions for any $K \in \mathbb{R}$ and $N \in [1,+\infty)$. In particular, this space is not a Ricci limit space. We also construct a compact non-collapsed strong Kato limit that cannot be obtained as Gromov-Hausdorff limit of closed Riemannian surfaces satisfying a uniform small $L^p$ bound à la Petersen--Wei. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_18097 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Strong Kato limit can be branching Carron, Gilles Mondello, Ilaria Tewodrose, David Differential Geometry We provide an example of a non-collapsed strong Kato limit that is branching, essentially branching, and satisfies neither the $\mathrm{CD}(K,\infty)$ nor the $\mathrm{MCP}(K,N)$ conditions for any $K \in \mathbb{R}$ and $N \in [1,+\infty)$. In particular, this space is not a Ricci limit space. We also construct a compact non-collapsed strong Kato limit that cannot be obtained as Gromov-Hausdorff limit of closed Riemannian surfaces satisfying a uniform small $L^p$ bound à la Petersen--Wei. |
| title | Strong Kato limit can be branching |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2411.18097 |