A connection between the Mahler conjecture and floating bodies

Agam Guberman

A connection between the Mahler conjecture and floating bodies

Metric Geometry 2026-08-11 v1

Authors: Agam Guberman

Abstract

In this paper, we will prove a result about the structure of polytopes whose floating bodies are not smooth. This will then be used to prove a result about the combinatorial structure of minimizers of the volume product.

Keywords

Mahler conjecture floating bodies polytopes volume product minimizers

Cite

@article{arxiv.2608.10994,
  title  = {A connection between the Mahler conjecture and floating bodies},
  author = {Agam Guberman},
  journal= {arXiv preprint arXiv:2608.10994},
  year   = {2026}
}