Isoperimetric problems for convex bodies and a localization lemma
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Our main tool is a general “Localization Lemma” that reduces integral inequalities over then-dimensional space to integral inequalities in a single variable. This lemma was first proved by two of the authors in an earlier paper, but here we give various extensions and variants that make its application smoother. We illustrate the usefulness of the lemma by showing how a number of well-known results can be proved using it.
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