Stability estimates for certain Faber-Krahn, isocapacitary and Cheeger inequalities

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Some methods for studying stability in isoperimetric type problems (2008, background): “There are many relevant variational problems [PS, Ka] intimately related to the same symmetrization inequalities studied here from a quantitative point of view, and these ideas have already been shown to be flexible enough to be employed in the study of quantitative forms of other variational proble”
A few shape optimization results for a biharmonic Steklov problem (2015, background): “We also refer to [21, 22] where these kind of questions have been considered for the ﬁrst time (see also [9, 18]).”
A Selection Principle for the Sharp Quantitative Isoperimetric Inequality (2010, background): “Since the publication of [19] the study of quantitative forms of various geometric and functional inequalities has received a new impulse (see for instance [8,13,14,18,20] and the review paper [26]).”