On the isoperimetric problem for radial log-convex densities

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Sharp isoperimetric inequalities via the ABP method (2013, unknown): “This question, and the associated isoperimetric inequalities with weights, have attracted much attention recently: see for example [43], [36], [17], [23], and [41].”
Sharp gradient stability for the Sobolev inequality (2020, background): “Introduction Motivated by important applications to problems in the calculus of variations and evolution PDEs, in recent years there has been a growing interest around the understanding of quantitative stability for functional/geometric inequalities, see for instance [3, 2, 8, 27, 28, 21, 9, 22, 29,”
Isoperimetry and Stability Properties of Balls with Respect to Nonlocal Energies (2014, methodology): “3, our proof is inspired by the strategy used in [16] (see also [15] for a related argument) to show the isoperimetry of balls in isoperimetric problems with log-convex densities.”
Higher-order Sobolev embeddings and isoperimetric inequalities (2013, background): “Let us limit ourselves to mentioning that, besides those quoted above, recent contributions on isoperimetric problems in (domains in) R endowed with a measure ν include [17,35,42,79].”