There are no geodesic hubs in the Brownian sphere

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 $k\ge 3$.

arXiv comment18 pages, 4 figures. arXiv admin note: text overlap with arXiv:2410.00426