A quantitative version of the isoperimetric inequality : the anisotropic case

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The sharp quantitative isoperimetric inequality (2008, result): “The next lemma is a variant of a similar result proved in [10] (see also [11]).”
Overdetermined anisotropic elliptic problems (2009, background): “More recent developments can be found in [3,10, 11 ,15,16,31].”
Some methods for studying stability in isoperimetric type problems (2008, methodology): “Starting from the seminal paper by Brezis and Lieb [BL], the reader will find various other contributions on quantitative geometric-functional inequalities based on similar or related tools [BE, Ci1, Ci2, CEFT, EFT , AFN].”
A Sharp Stability Result for the Relative Isoperimetric Inequality Inside Convex Cones (2012, background): “For the general case when K is a generic convex set, non-sharp results were obtained by Esposito, Fusco, Trombetti [14], while the sharp estimate was recently obtained by Figalli, Maggi, Pratelli [16].”
A mass transportation approach to quantitative isoperimetric inequalities (2010, result): “Under the assumption of convexity on E, the problem has been studied by Groemer [27], while the first stability result for (1.4) on generic sets is due to Esposito, Fusco, and Trombetti in [ 18 ].”