On Lieb’s “On the lowest eigenvalue of the Laplacian for the intersection of two domains”

Abstract

We review the results and impact of the paper of our title. In particular, we try to give a sense of how others have built onto or extended Lieb’s work in this area. We also expand upon some simple examples that Lieb gave to demonstrate the sharpness of his results and fill in the details of one piece of the history of “inradius lower bounds for the principal eigenvalue” with which the author was involved personally.