A surface with discontinuous isoperimetric profile and expander manifolds

Author: 

Papasoglu, P
Swenson, E

Publication Date: 

June 2020

Journal: 

GEOMETRIAE DEDICATA

Last Updated: 

2020-07-06T02:02:58.13+01:00

Issue: 

1

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 $\epsilon ,
M>0$ 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 $\epsilon $, has area greater than $M$.

Symplectic id: 

544848

Download URL: 

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article