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The α-Cosine Transform and Intertwining Integrals on Real Grassmannians Read chapter Read first chapter

2012 | OriginalPaper | Chapter

Remark on Stability of Brunn–Minkowski and Isoperimetric Inequalities for Convex Bodies

Author : Alexander Segal

Published in: Geometric Aspects of Functional Analysis

Publisher: Springer Berlin Heidelberg

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Abstract

This paper is a note on the work of Figalli, Maggi and Pratelli, regarding the stability of Brunn–Minkowski and the isoperimetric inequalities. By a careful examination of the methods presented in the mentioned papers, we slightly improve the constants that appear in stability versions of these inequalities, which play an important role in asymptotic geometric analysis. In addition we discuss a stability version of Urysohn’s inequality and the relation to Dar’s conjecture.

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previous chapter Approximate Gaussian Isoperimetry for k Sets
next chapter On Contact Points of Convex Bodies
Literature
1.
2.
Y. Brenier, Polar factorization and monotone rearrangement of vector-valued functions. Comm. Pure Appl. Math. 44(4), 375–417 (1991)MathSciNetMATHCrossRef
3.
Yu.D. Burago, V.A. Zalgaller, Geometric Inequalities. A series of comprehensive studies in mathematics (Springer-Verlag, Berlin, 1980)
4.
5.
L.A. Caffarelli, Boundary regularity of maps with convex potentials. II. Ann. of Math. (2) 144(3), 453–496 (1996)
6.
7.
V.I. Diskant, Stability of the solution of a Minkowski equation (Russian). Sibirsk. Mat. Z. 14, 669–673, 696 (1973)
8.
A. Figalli, F. Maggi, F. Pratelli, A refined Brunn-Minkowski inequality for convex sets. Ann. Inst. H. Poincaré Anal. Non Linaire 26(6), 2511–2519 (2009)MathSciNetMATHCrossRef
9.
A. Figalli, F. Maggi, F. Pratelli, A mass transportation approach to quantitative isoperimetric inequalities. Invent. Math. 182(1), 167–211 (2010)MathSciNetMATHCrossRef
10.
R. Gardner, Geometric Tomography, 2nd edn. (Cambridge University Press, London, 2006)MATH
11.
F. John, An inequality for convex bodies. Univ. Kentucky Res. Club Bull. 8, 8–11 (1942)
12.
R. Schneider, Convex Bodies: The Brunn Minkowski Theory (Cambridge University Press, London, 1993)MATHCrossRef
13.
C. Villani, in Topics in Optimal Transportation. Graduate Studies in Mathematics, vol. 58 (American Mathematical Society, Providence, 2003)
Metadata
Title
Remark on Stability of Brunn–Minkowski and Isoperimetric Inequalities for Convex Bodies
Author
Alexander Segal
Copyright Year
2012
Publisher
Springer Berlin Heidelberg
Book
Geometric Aspects of Functional Analysis

Print ISBN: 978-3-642-29848-6

Electronic ISBN: 978-3-642-29849-3

Copyright Year: 2012

DOI
https://doi.org/10.1007/978-3-642-29849-3_24

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