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.
Rigidity of equality cases in Steiner's perimeter inequality / Filippo Cagnetti; Maria Colombo; Guido De Philippis; Francesco Maggi. - In: ANALYSIS & PDE. - ISSN 1948-206X. - ELETTRONICO. - 7:(2014), pp. 1535-1593. [10.2140/apde.2014.7.1535]
Rigidity of equality cases in Steiner's perimeter inequality
MAGGI, FRANCESCO
2014
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.I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.