A surface with discontinuous isoperimetric profile and expander manifolds

Author: 

Papazoglou, P
Swenson, E

Publication Date: 

3 August 2019

Journal: 

Geometriae Dedicata

Last Updated: 

2020-07-18T03:54:21.733+01:00

Volume: 

206

DOI: 

10.1007/s10711-019-00475-9

page: 

43–54-

abstract: 

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 ǫ, 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 ǫ, has area greater than

Symplectic id: 

1033703

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article