# A surface with discontinuous isoperimetric profile and expander manifolds

Papasoglu, P
Swenson, E

June 2020

## Journal:

GEOMETRIAE DEDICATA

## Last Updated:

2021-07-02T17:46:32.95+01:00

1

206

## DOI:

10.1007/s10711-019-00475-9

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 $M$.

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