English

Rigidity of equality cases in Steiner's perimeter inequality

Analysis of PDEs 2016-01-20 v1 Metric Geometry Optimization and Control

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's 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 an hyperplane.

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Cite

@article{arxiv.1309.1639,
  title  = {Rigidity of equality cases in Steiner's perimeter inequality},
  author = {Filippo Cagnetti and Maria Colombo and Guido De Philippis and Francesco Maggi},
  journal= {arXiv preprint arXiv:1309.1639},
  year   = {2016}
}

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53 pages