Strong Kato limit can be branching

2024/11/27 by Gilles Carron, Carron, Gilles, Ilaria Mondello +3
Biochemistry, Genetics and Molecular Biology · Engineering · Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Gene Regulatory Network Analysis #Mathematical Biology Tumor Growth #Slime Mold and Myxomycetes Research

paper · pdf · doi:10.48550/arxiv.2411.18097

openalex publication_date 2024/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

We provide an example of a non-collapsed strong Kato limit that is branching, essentially branching, and satisfies neither the CD(K,∞) nor the MCP(K,N) conditions for any K ∈ ℝ and N ∈ [1,+∞). 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.

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