Steiner symmetrization does not increase the perimeter of sets in R^n. In this paper we investigate for which sets the perimeter is preserved under symmetrization. In contrast to Schwarz symmetrization, where only balls preserve perimeter, sets that preserve perimeter under Steiner symmetrization need not be Steiner-symmetric before symmetrization.
The perimeter inequality under Steiner symmetrization: cases of equality / M. CHLEBIK; A. CIANCHI; N. FUSCO. - In: ANNALS OF MATHEMATICS. - ISSN 0003-486X. - STAMPA. - 162:(2005), pp. 525-555.
The perimeter inequality under Steiner symmetrization: cases of equality
CIANCHI, ANDREA;
2005
Abstract
Steiner symmetrization does not increase the perimeter of sets in R^n. In this paper we investigate for which sets the perimeter is preserved under symmetrization. In contrast to Schwarz symmetrization, where only balls preserve perimeter, sets that preserve perimeter under Steiner symmetrization need not be Steiner-symmetric before symmetrization.File in questo prodotto:
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