Eigenvalue Inequalities

Following Chapter 5 of Levitin–Mangoubi–Polterovich, we will survey three classical eigenvalue inequalities for the Laplacian: the Faber–Krahn, Cheeger, and Szegő–Weinberger inequalities. We will then focus on the Faber–Krahn inequality, giving a proof, discussing (quantitative) stability, and presenting a few applications.