Vertical versus horizontal isoperimetry

We will explain an isoperimetric-type inequality for subsets of the Heisenberg group that controls the size of the (suitably defined) vertical boundary by the perimeter. This inequality was conceived for a specific application that we will describe, but in the course of its investigation there were twists and turns that unearthed unexpected geometric phenomena and led to further applications to longstanding questions. These will be explained, but the main purpose of this talk is to show the geometric structures that arise in the proof.

https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09