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.
Keywords
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