Archive for 26th July 2013

Isoperimetric Profile Continuous?

26th July 2013, 05:39 am

Note added 5 June 2016. A noncompact counterexample is given by Nardulli and Pansu, arxiv.org. On the positive side, see the comment below by Milman and Flores/Nardulli [FN].

Note added 21 March 2018. A 2D (noncompact) counterexample is given by Papasoglu and Swenson [PS], via expander graphs.

Given a smooth Riemannian manifold, the isoperimetric profile I(V) gives the infimum perimeter of smooth regions of volume V.

Proposition 1. In a compact smooth Riemannian manifold of dimension at least two, the isoperimetric profile is continuous. Continue reading ‘Isoperimetric Profile Continuous?’ »

Category: Math  |  1 Comment