26 citations · 63 across the 24 of their papers we have counts for
6 papers · 1 filter
Uryson width and volume
Panos Papasoglu
We give a short proof of a theorem of Guth relating volume of balls and Uryson width. The same approach applies to Hausdorff content implying a recent result of Liokumovich-Lishak-…
A surface with discontinuous isoperimetric profile
Panos Papasoglu, Eric Swenson
We show that there is a complete connected 2-dimensional Riemannian manifold with discontinuous isoperimetric profile, answering a question of Nardulli and Pansu.
Short loops in surfaces with a circle boundary component
Panos Papasoglu
It is a classical theorem of Loewner that the systole of a Riemannian torus can be bounded in terms of its area. We answer a question of a similar flavor of Robert Young showing th…
A surface with discontinuous isoperimetric profile and expander manifolds
Panos Papasoglu, Eric Swenson
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…
Contracting thin disks
Panos Papasoglu
We answer a question of Liokumovich-Nabutovsky-Rotman showing that if D is a Riemannian 2-disc with boundary length L, diameter d and area A << d then D can be filled by a homotopy…
Cheeger constants of surfaces and isoperimetric inequalities
Panos Papasoglu
We show that the Cheeger constant of compact surfaces is bounded by a function of the area. We apply this to isoperimetric profiles of bounded genus non-compact surfaces, to show t…