Inserted: 16 apr 2016
Last Updated: 5 jun 2017
This is a chapter of the forthcoming book "Shape Optimization and Spectral Theory", edited by Antoine Henrot and published by De Gruyter.
We review some results about quantitative improvements of sharp inequalities for eigenvalues of the Laplacian.
Keywords: Stability of eigenvalues, Szego-Weinberger, Torsional rigidity, Faber-Krahn, Brock-Weinstock, Hong-Krahn-Szego, harmonic radius, Ashbaugh-Benguria