Rearrangements in Carnot Groups
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KeywordsSymmetrization rearrangements Carnot groups
MR(2010) Subject Classification30C65 42B31
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Part of this work was done while the first author visited the Universidad Nacional de Cuyo as a FOMEC visiting professor during the Summers of 1998 and 2000. He wishes to express his appreciation for the kind hospitality and the nice working atmosphere.
We did not submit this manuscript for publication because we were trying to proof the sharp version of Theorem 5; that is Cper = 1, which to the best of our knowledge remains open as of today. Nevertheless, the preprint was circulated among the community. We received several requests from colleagues, and it has been quoted several times in the literature. See for example the book , the dissertation , and the papers [4, 6, 11–13, 19], and . In addition, the main results have not been published elsewhere. This is why we decided to submit this manuscript to publication. We are very thankful to Acta Mathematica Sinica, English Series for considering this manuscript.
We are thankful to the referees for the careful reading and thoughtful suggestions.
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