2022/11/11 by Alpert, Hannah
#53C23 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2211.06362
We use Papasoglu's method of area-minimizing separating sets to give an alternative proof, and explicit constants, for the following theorem of Guth and Braun--Sauer: If M is a closed, oriented, n-dimensional manifold, with a Riemannian metric such that every ball of radius 1 in the universal cover of M has volume at most V1, then the simplicial volume of M is at most the volume of M times a constant depending on n and V1.