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arxiv:2501.02571
There are no geodesic hubs in the Brownian sphere
Published on Jan 5
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Abstract
In the Brownian sphere, no point can serve as a 3-hub or higher, meaning it cannot be the endpoint of three or more disjoint geodesics with the concatenation property.
AI-generated summary
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 kgeq 3.
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