The quantitative isoperimetric inequality and related topics

By N. Fusco. 2015

94 citations recorded by the source corpus.

We present some recent stability results concerning the isoperimetric inequality and other related geometric and functional inequalities. The main techniques and approaches to this field are discussed.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/8439abb2a30492177a520e5e0337635e23974b92

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In Applied Mathematics

1. Y. Zhang
2. Fabio Di Nicola
3. Alessio Figalli
4. Paolo Tilli
5. Guido De Philippis
6. Max Fathi
7. Dario Trevisan
8. Robert J. McCann

Citations in the corpus

• The Faber–Krahn inequality for the short-time Fourier transform (2021, methodology): “Following the same pattern as in Proposition 3.3, now using the isoperimetric inequality in R 2 d (see e.g. [30] for an updated account) and the fact that log u = − 4 πd on { u > 0 } , we see that now u ∗ satisfies the inequality s ) for a.e. s > 0 in place of (3.13), and hence (3.14) is to be…”
• Sharp gradient stability for the Sobolev inequality (2020, methodology): “These technique were further developed by Figalli, Maggi, and Pratelli in [23] to provide a sharp stability result —both in terms of the notion of distance and of the decay exponent— in the special case p = 1 (for this case, see also the earlier results [8, 26, 27]).”