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Rigidity of equality cases in Steiner's perimeter inequality

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journal contribution
posted on 2023-06-08, 18:44 authored by Filippo Cagnetti, Maria Colombo, Guido De Philippis, Francesco Maggi
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.

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Analysis and PDE

ISSN

2157-5045

Publisher

Mathematical Sciences Publishers

Issue

7

Volume

7

Page range

1535-1593

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2014-10-20

First Open Access (FOA) Date

2014-10-20

First Compliant Deposit (FCD) Date

2014-10-20

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