2022/05/27 by Li, Xinze, Staffa, Bruno · 1 citation
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.2205.13694
We show that given a closed n-manifold M, for a generic set of Riemannian metrics g on M there exists a sequence of closed geodesics that are equidistributed in M if n=2; and an equidistributed sequence of embedded stationary geodesic nets if n=3. One of the main tools that we use is the Weyl Law for the volume spectrum for 1-cycles, proved by Liokumovich, Marques and Neves for n=2 and more recently by Guth and Liokumovich for n=3. We show that our proof of the equidistribution of geodesic nets can be generalized for any dimension n≥ 2 provided the Weyl Law for 1-cycles in n-manifolds holds.