Inserted: 24 apr 2015
Last Updated: 24 apr 2015
This is an expository article showing some 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.