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A Semigroup Version of the Isoperimetric Inequality

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Abstract

In this article we extend the heat semigroup version of the isoperimetric inequality in Rn established by M. Ledoux. To this purpose, the notion of the perimeter of a Caccioppoli set introduced by E. De Giorgi yields the appropriate measure theoretical background. In the proofs we use properties of the heat semigroup as well as its explicit integral representation.

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  1. Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany

    Marc Preunkert

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  1. Marc Preunkert
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Correspondence to Marc Preunkert.

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Edited by Jerome A. Goldstein

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Preunkert, M. A Semigroup Version of the Isoperimetric Inequality. Semigroup Forum 68, 233–245 (2004). https://doi.org/10.1007/s00233-003-0004-1

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  • DOI: https://doi.org/10.1007/s00233-003-0004-1

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