Brunn–Minkowski theorem

Known as: Brunn minkowski inequality, Brunn–Minkowski inequality, Brunn-minkowski inequality 
In mathematics, the Brunn–Minkowski theorem (or Brunn–Minkowski inequality) is an inequality relating the volumes (or more generally Lebesgue… (More)
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Highly Cited
2014
Highly Cited
2014
The Brunn Minkowski theory is the heart of quantitative convexity. It had its origins in Minkowski's joining his notion of mixed… (More)
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2014
2014
The Brunn-Miknowski inequality gives a lower bound on the Lebesgue measure of a sumset in terms of the measures of the individual… (More)
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2013
2013
For origin-symmetric convex bodies (i.e., the unit balls of finite dimensional Banach spaces) it is conjectured that there exist… (More)
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2009
2009
Starting from a mass transportation proof of the Brunn-Minkowski inequality on convex sets, we improve the inequality showing a… (More)
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2008
2008
A detailed investigation is undertaken into Brunn-Minkowski-type inequalities for Gauss measure. A Gaussian dual Brunn-Minkowski… (More)
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Highly Cited
2008
Highly Cited
2008
The concept of a miss-distance, or error, between a reference quantity and its estimated/controlled value, plays a fundamental… (More)
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2006
2006
The Brunn–Minkowski inequality gives a lower bound of the Lebesgue measure of a sum-set in terms of the measures of the… (More)
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2006
2006
Suppose two bounded subsets of R are given. Parametrise the Minkowski combination of these sets by t. The Classical Brunn… (More)
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2005
2005
Theorem 7.1 (Brunn-Minkowski). If A, B ⊆ R n satisfy some mild assumptions (in particular, convexity suffices), then [vol (A + B… (More)
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Review
2001
Review
2001
In 1978, Osserman [124] wrote a rather comprehensive survey on the isoperimetric inequality. The Brunn-Minkowski inequality can… (More)
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