2015/09/08 by Panos Papasoglu, Papasoglu, Panos, Eric Swenson +1 · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG
paper · pdf · doi:10.48550/arxiv.1509.02307
15 pages, this paper merged with arXiv:1803.07375 (2018), to appear in Geom. Dedicata
arxiv created 2019/07/21 · arxiv updated 2019/07/23
We construct sequences of `expander manifolds' and we use them to show that there is a complete connected 2-dimensional Riemannian manifold with discontinuous isoperimetric profile, answering a question of Nardulli and Pansu. Using expander manifolds in dimension 3 we show that for any ε, M>0 there is a Riemannian 3-sphere S of volume 1, such that any (not necessarily connected) surface separating S in two regions of volume greater than ε, has area greater than M.