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2014 Rigidity of equality cases in Steiner's perimeter inequality
Filippo Cagnetti, Maria Colombo, Guido De Philippis, Francesco Maggi
Anal. PDE 7(7): 1535-1593 (2014). DOI: 10.2140/apde.2014.7.1535

Abstract

Characterization results for equality cases and for rigidity of equality cases in Steiner’s perimeter inequality are presented. (By rigidity, we mean the situation when all equality cases are vertical translations of the Steiner symmetral under consideration.) We achieve this through the introduction of a suitable measure-theoretic notion of connectedness and a fine analysis of barycenter functions for sets of finite perimeter having segments as orthogonal sections with respect to a hyperplane.

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Filippo Cagnetti. Maria Colombo. Guido De Philippis. Francesco Maggi. "Rigidity of equality cases in Steiner's perimeter inequality." Anal. PDE 7 (7) 1535 - 1593, 2014. https://doi.org/10.2140/apde.2014.7.1535

Information

Received: 6 September 2013; Revised: 25 June 2014; Accepted: 11 August 2014; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1327.49069
MathSciNet: MR3293444
Digital Object Identifier: 10.2140/apde.2014.7.1535

Subjects:
Primary: 49K21

Keywords: equality cases , rigidity , symmetrization

Rights: Copyright © 2014 Mathematical Sciences Publishers

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