The Experts below are selected from a list of 7293 Experts worldwide ranked by ideXlab platform
Nicola Fusco - One of the best experts on this subject based on the ideXlab platform.
-
A quantitative Isoperimetric Inequality on the sphere
Advances in Calculus of Variations, 2017Co-Authors: Verena Bögelein, Frank Duzaar, Nicola FuscoAbstract:In this paper we prove a quantitative version of the Isoperimetric Inequality on the sphere with a constant independent of the volume of the set E.
-
The Stability of the Isoperimetric Inequality
Lecture Notes in Mathematics, 2017Co-Authors: Nicola FuscoAbstract:These lecture notes contain the material that I presented in two summer courses in 2013, one at the Carnegie Mellon University and the other one in a CIME school at Cetraro. The aim of both courses was to give a quick but comprehensive introduction to some recent results on the stability of the Isoperimetric Inequality.
-
The quantitative Isoperimetric Inequality and related topics
Bulletin of Mathematical Sciences, 2015Co-Authors: Nicola FuscoAbstract: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.
-
A strong form of the Quantitative Isoperimetric Inequality
Calculus of Variations and Partial Differential Equations, 2013Co-Authors: Nicola Fusco, Vesa JulinAbstract:We give a refinement of the quantitative Isoperimetric Inequality. We prove that the Isoperimetric gap controls not only the Fraenkel asymmetry but also the oscillation of the boundary.
-
A quantitative Isoperimetric Inequality for fractional perimeters
Journal of Functional Analysis, 2011Co-Authors: Nicola Fusco, Vincent Millot, Massimiliano MoriniAbstract:Abstract Recently Frank and Seiringer have shown an Isoperimetric Inequality for nonlocal perimeter functionals arising from Sobolev seminorms of fractional order. This Isoperimetric Inequality is improved here in a quantitative form.
Sasha Sodin - One of the best experts on this subject based on the ideXlab platform.
-
an Isoperimetric Inequality for uniformly log concave measures and uniformly convex bodies
Journal of Functional Analysis, 2008Co-Authors: Emanuel Milman, Sasha SodinAbstract:Abstract We prove an Isoperimetric Inequality for the uniform measure on a uniformly convex body and for a class of uniformly log-concave measures (that we introduce). These inequalities imply (up to universal constants) the log-Sobolev inequalities proved by Bobkov, Ledoux [S.G. Bobkov, M. Ledoux, From Brunn–Minkowski to Brascamp–Lieb and to logarithmic Sobolev inequalities, Geom. Funct. Anal. 10 (5) (2000) 1028–1052] and the Isoperimetric inequalities due to Bakry, Ledoux [D. Bakry, M. Ledoux, Levy–Gromov's Isoperimetric Inequality for an infinite-dimensional diffusion generator, Invent. Math. 123 (2) (1996) 259–281] and Bobkov, Zegarlinski [S.G. Bobkov, B. Zegarlinski, Entropy bounds and isoperimetry, Mem. Amer. Math. Soc. 176 (829) (2005), x+69]. We also recover a concentration Inequality for uniformly convex bodies, similar to that proved by Gromov, Milman [M. Gromov, V.D. Milman, Generalization of the spherical Isoperimetric Inequality to uniformly convex Banach spaces, Compos. Math. 62 (3) (1987) 263–282].
-
an Isoperimetric Inequality for uniformly log concave measures and uniformly convex bodies
Journal of Functional Analysis, 2008Co-Authors: Emanuel Milman, Sasha SodinAbstract:Abstract We prove an Isoperimetric Inequality for the uniform measure on a uniformly convex body and for a class of uniformly log-concave measures (that we introduce). These inequalities imply (up to universal constants) the log-Sobolev inequalities proved by Bobkov, Ledoux [S.G. Bobkov, M. Ledoux, From Brunn–Minkowski to Brascamp–Lieb and to logarithmic Sobolev inequalities, Geom. Funct. Anal. 10 (5) (2000) 1028–1052] and the Isoperimetric inequalities due to Bakry, Ledoux [D. Bakry, M. Ledoux, Levy–Gromov's Isoperimetric Inequality for an infinite-dimensional diffusion generator, Invent. Math. 123 (2) (1996) 259–281] and Bobkov, Zegarlinski [S.G. Bobkov, B. Zegarlinski, Entropy bounds and isoperimetry, Mem. Amer. Math. Soc. 176 (829) (2005), x+69]. We also recover a concentration Inequality for uniformly convex bodies, similar to that proved by Gromov, Milman [M. Gromov, V.D. Milman, Generalization of the spherical Isoperimetric Inequality to uniformly convex Banach spaces, Compos. Math. 62 (3) (1987) 263–282].
Gian Paolo Leonardi - One of the best experts on this subject based on the ideXlab platform.
-
A Selection Principle for the Sharp Quantitative Isoperimetric Inequality
Archive for Rational Mechanics and Analysis, 2012Co-Authors: Marco Cicalese, Gian Paolo LeonardiAbstract:We introduce a new variational method for the study of Isoperimetric inequalities with quantitative terms. The method is general as it relies on a penalization technique combined with the regularity theory for quasiminimizers of the perimeter. Two notable applications are presented. First we give a new proof of the sharp quantitative Isoperimetric Inequality in \({\mathbb{R}^n}\). Second we positively answer a conjecture by Hall concerning the best constant for the quantitative Isoperimetric Inequality in \({\mathbb{R}^2}\) in the small asymmetry regime.
-
A Selection Principle for the Sharp Quantitative Isoperimetric Inequality
arXiv: Analysis of PDEs, 2010Co-Authors: Marco Cicalese, Gian Paolo LeonardiAbstract:We introduce a new variational method for the study of stability in the Isoperimetric Inequality. The method is quite general as it relies on a penalization technique combined with the regularity theory for quasiminimizers of the perimeter. Two applications are presented. First we give a new proof of the sharp quantitative Isoperimetric Inequality in $R^n$. Second we positively answer to a conjecture by Hall concerning the best constant for the quantitative Isoperimetric Inequality in $R^2$ in the small asymmetry regime.
Vesa Julin - One of the best experts on this subject based on the ideXlab platform.
-
sharp dimension free quantitative estimates for the gaussian Isoperimetric Inequality
Annals of Probability, 2017Co-Authors: Marco Barchiesi, Alessio Brancolini, Vesa JulinAbstract:We provide a full quantitative version of the Gaussian Isoperimetric Inequality: the difference between the Gaussian perimeter of a given set and a half-space with the same mass controls the gap between the norms of the corresponding barycenters. In particular, it controls the Gaussian measure of the symmetric difference between the set and the half-space oriented so to have the barycenter in the same direction of the set. Our estimate is independent of the dimension, sharp on the decay rate with respect to the gap and with optimal dependence on the mass.
-
sharp dimension free quantitative estimates for the gaussian Isoperimetric Inequality
arXiv: Analysis of PDEs, 2014Co-Authors: Marco Barchiesi, Alessio Brancolini, Vesa JulinAbstract:We provide a full quantitative version of the Gaussian Isoperimetric Inequality. Our estimate is independent of the dimension, sharp on the decay rate with respect to the asymmetry and with optimal dependence on the mass.
-
A strong form of the Quantitative Isoperimetric Inequality
Calculus of Variations and Partial Differential Equations, 2013Co-Authors: Nicola Fusco, Vesa JulinAbstract:We give a refinement of the quantitative Isoperimetric Inequality. We prove that the Isoperimetric gap controls not only the Fraenkel asymmetry but also the oscillation of the boundary.
Emanuel Milman - One of the best experts on this subject based on the ideXlab platform.
-
an Isoperimetric Inequality for uniformly log concave measures and uniformly convex bodies
Journal of Functional Analysis, 2008Co-Authors: Emanuel Milman, Sasha SodinAbstract:Abstract We prove an Isoperimetric Inequality for the uniform measure on a uniformly convex body and for a class of uniformly log-concave measures (that we introduce). These inequalities imply (up to universal constants) the log-Sobolev inequalities proved by Bobkov, Ledoux [S.G. Bobkov, M. Ledoux, From Brunn–Minkowski to Brascamp–Lieb and to logarithmic Sobolev inequalities, Geom. Funct. Anal. 10 (5) (2000) 1028–1052] and the Isoperimetric inequalities due to Bakry, Ledoux [D. Bakry, M. Ledoux, Levy–Gromov's Isoperimetric Inequality for an infinite-dimensional diffusion generator, Invent. Math. 123 (2) (1996) 259–281] and Bobkov, Zegarlinski [S.G. Bobkov, B. Zegarlinski, Entropy bounds and isoperimetry, Mem. Amer. Math. Soc. 176 (829) (2005), x+69]. We also recover a concentration Inequality for uniformly convex bodies, similar to that proved by Gromov, Milman [M. Gromov, V.D. Milman, Generalization of the spherical Isoperimetric Inequality to uniformly convex Banach spaces, Compos. Math. 62 (3) (1987) 263–282].
-
an Isoperimetric Inequality for uniformly log concave measures and uniformly convex bodies
Journal of Functional Analysis, 2008Co-Authors: Emanuel Milman, Sasha SodinAbstract:Abstract We prove an Isoperimetric Inequality for the uniform measure on a uniformly convex body and for a class of uniformly log-concave measures (that we introduce). These inequalities imply (up to universal constants) the log-Sobolev inequalities proved by Bobkov, Ledoux [S.G. Bobkov, M. Ledoux, From Brunn–Minkowski to Brascamp–Lieb and to logarithmic Sobolev inequalities, Geom. Funct. Anal. 10 (5) (2000) 1028–1052] and the Isoperimetric inequalities due to Bakry, Ledoux [D. Bakry, M. Ledoux, Levy–Gromov's Isoperimetric Inequality for an infinite-dimensional diffusion generator, Invent. Math. 123 (2) (1996) 259–281] and Bobkov, Zegarlinski [S.G. Bobkov, B. Zegarlinski, Entropy bounds and isoperimetry, Mem. Amer. Math. Soc. 176 (829) (2005), x+69]. We also recover a concentration Inequality for uniformly convex bodies, similar to that proved by Gromov, Milman [M. Gromov, V.D. Milman, Generalization of the spherical Isoperimetric Inequality to uniformly convex Banach spaces, Compos. Math. 62 (3) (1987) 263–282].
