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A pair of subsets of Euclidean space which nearly achieves equality in the Brunn-Minkowski inequality must nearly coincide with a pair of homothetic convex sets.
F. Riesz, Sur une inégalité intégrale
1930
Earlier work this paper cites.
R. Henstock and A. M. Macbeath, On the measure of sum-sets. I. The theorems of Brunn, Minkowski, and Lusternik
1953
Earlier work this paper cites.
H. Hadwiger and D. Ohmann, Brunn-Minkowskischer Satz und Isoperimetrie
1956
Earlier work this paper cites.
S. L. Sobolev, On a theorem of functional analysis
1963
Cited alongside, same era.
by same author Near equality in the two-dimensional Brunn-Minkowski inequality
1965
Cited alongside, same era.
A. Burchard, Cases of equality in the Riesz rearrangement inequality
1996
Cited alongside, same era.
M. Charalambides and M. Christ, Near–extremizers for Young’s inequality for discrete groups
Cited in the paper.
M. Christ, Extremizers of a Radon transform inequality
Cited in the paper.
by same author An approximate inverse Riesz-Sobolev rearrangement inequality
Cited in the paper.
by same author On near-extremizers for Young’s inequality for ℝ d {\mathbb{R}}^{d}
Cited in the paper.
E. H. Lieb and M. Loss, Analysis
1997
Later among the works it cites.
R. J. Gardner, The Brunn-Minkowski inequality
2002
Later among the works it cites.
T. Tao and V. Vu, Additive Combinatorics
2006
Later among the works it cites.
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