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arXiv · 2411.18097

Strong Kato limit can be branching

Gilles Carron·Ilaria Mondello·David Tewodrose
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Abstract

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 \`a la Petersen--Wei.

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Gilles Carron, Ilaria Mondello, David Tewodrose. 2024-11-27. Strong Kato limit can be branching. https://arxiv.org/abs/2411.18097

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