Geodesic
The perimeter inequality under Steiner symmetrization: Cases of equality
Miroslav Chlebík1 ; Andrea Cianchi2 ; Nicola Fusco3
1Max-Planck-Institut für Mathematik in den Naturwissenschaften, 04103 Leipzig, Germany
2Dipartimento di Matematica, Università degli Studi di Firenze, 50134 Firenze, taly
3Facoltà di Scienze Matematiche Fisiche e Naturali, Università degli Studi di Napoli, 80126 Napoli, Italy
Annals of mathematics, Tome 162 (2005) no. 1, pp. 525-555
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Steiner symmetrization is known not to increase perimeter of sets in $\mathbb{R}^n$. The sets whose perimeter is preserved under this symmetrization are characterized in the present paper.

DOI : 10.4007/annals.2005.162.525

Miroslav Chlebík  1   ; Andrea Cianchi  2   ; Nicola Fusco  3

1 Max-Planck-Institut für Mathematik in den Naturwissenschaften, 04103 Leipzig, Germany
2 Dipartimento di Matematica, Università degli Studi di Firenze, 50134 Firenze, taly
3 Facoltà di Scienze Matematiche Fisiche e Naturali, Università degli Studi di Napoli, 80126 Napoli, Italy 
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Miroslav Chlebík; Andrea Cianchi; Nicola Fusco. The perimeter inequality under Steiner symmetrization: Cases of equality. Annals of mathematics, Tome 162 (2005) no. 1, pp. 525-555. doi: 10.4007/annals.2005.162.525

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