The sharp quantitative isoperimetric inequality

By N. Fusco, Francesco Maggi, Aldo Pratelli. 2008

444 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/b96ee796ca85b2586fe55676893d9f4e90fc9ad0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

Citations in the corpus

Nonlocal quantitative isoperimetric inequalities (2015, background): “A cornerstone example has been given in the paper [23] where the authors show an inequality of the form”
Local $L^p$-Brunn-Minkowski inequalities for $p<1$ (2017, methodology): “The approach in [21] was based on a careful analysis of symmetrization of K, and thus confined to the isotropic case L = Bn 2 .”
Droplet Minimizers of an Isoperimetric Problem with Long‐Range Interactions (2011, background): “The following, called sharp quantitative isoperimetric inequality, has been proved in [17, 23, 25].”
Sets of Finite Perimeter and Geometric Variational Problems: An Introduction to Geometric Measure Theory (2012, background): “The work with Nicola Fusco and Aldo Pratelli on the stability of the Euclidean isoperimetric inequality [FMP08] greatly influenced the point of view on sets of finite perimeter adopted in this book, which has also been crucially shaped (particularly in connection with the regularity theory of Part I”
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,”
New approach to the affine P\'olya-Szeg\"o principle and the stability version of the affine Sobolev inequality (2015, background): “We refer the reader to [2, 3, 4, 5, 10, 11, 12, 19, 21, 22, 23, 24, 25, 26] and references therein for more background and results in this direction.”
A User’s Guide to Optimal Transport (2013, methodology): “The use of Brenier’s map instead of Knothe’s one makes the difference when studying the quantitative version of the isoperimetric problem: Figalli, Maggi and Pratelli in [38], using tools coming from optimal transport, proved the sharp quantitative isoperimetric inequality in R endowed with any norm”
Stability of the Steiner symmetrization of convex sets (2013, background): “In recent years quantitative isoperimetric and related functional inequalities have attracted the interest of several authors ([8, 11, 12, 13, 14, 15], to name but a few).”
Some methods for studying stability in isoperimetric type problems (2008, result): “inequality is implied by Hall’s theorem, and an alternative proof is found in [ FMP1 ].”
Local Lp-Brunn-Minkowski inequalities for p<1 (2017, methodology): “can obtain stable versions of these inequalities, lower bounding the deﬁcits δ(K,L) and β(K,L) by some function of A(K,L). In a groundbreaking work, it was shown by N. Fusco, F. Maggi and A. Pratelli [21] in the isotropic case (when L = Bn 2 ), that for all Borel sets K in Rn of ﬁnite perimeter: δ(K”
Sharp Stability of Some Spectral Inequalities (2012, background): “For more details, historical remarks and a comprehensive bibliography on other stability results for the aforementioned inequalities, the reader is referred to the papers [5] and [6].”
Isoperimetry and Stability Properties of Balls with Respect to Nonlocal Energies (2014, methodology): “Letting s → 1 we recover the sharp stability result for the classical perimeter, that was first proved in [22] by symmetrization methods and later extended to anisotropic perimeters in [17] by mass transportation.”
The Faber–Krahn inequality for the short-time Fourier transform (2021, background): “…derivative of µ ( t ) (which ultimately make the validity of (3.11) highly nontrivial), and in fact the seminal paper [13] was motivated by a subtle error in a previous work, whose ﬁxing since [13] has stimulated a lot of original and deep research (see e.g. [15, 31] and references therein).”