Calculus of Variations and Geometric Measure Theory

G. P. Leonardi

An overview on the Cheeger problem

created by leonardi on 24 Apr 2015
modified on 31 Jan 2024



Inserted: 24 apr 2015
Last Updated: 31 jan 2024

Year: 2015

ArXiv: 1504.06264 PDF


This is an expository article presenting various results about the Cheeger problem and its connections with other relevant mathematical problems. In section 2 we synthetically describe three mathematical problems (eigenvalue estimates, prescribed mean curvature equation, ROF model for image segmentation) focusing on their link with the Cheeger problem. Then, a selection of classical as well as more recent results obtained in collaboration with Aldo Pratelli will be described in the remaining sections.