There are no geodesic hubs in the Brownian sphere

Mathieu Mourichoux

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arXiv · 2501.02571

There are no geodesic hubs in the Brownian sphere

Mathieu Mourichoux

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Abstract

A point of a metric space is called a $k$-hub if it is the endpoint of exactly $k$ disjoint geodesics, and that the concatenation of any two of these paths is still a geodesic. We prove that in the Brownian sphere, there is no $k$-hub for $k\geq 3$.

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Mathieu Mourichoux. 2025-01-05. There are no geodesic hubs in the Brownian sphere. https://arxiv.org/abs/2501.02571

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