@article{d5bd8783781c44a3a41d84f58853cdd9,
title = "Essential connectedness and the rigidity problem for Gaussian symmetrization",
abstract = "We provide a geometric characterization of rigidity of equality cases in Ehrhard's symmetrization inequality for Gaussian perimeter. This condition is formulated in terms of a new measure-theoretic notion of connectedness for Borel sets, inspired by Federer's definition of indecomposable current, and of possible broader interest.",
keywords = "Equality cases, Gauss space, Rigidity, Symmetrization",
author = "Filippo Cagnetti and Maria Colombo and {De Philippis}, Guido and Francesco Maggi",
note = "Funding Information: This work was carried out while FC, MC, and GDP were visiting the University of Texas at Austin. The work of FC was partially supported by the UT Austin-Portugal partnership through the FCT post-doctoral fellowship SFRH/BPD/51349/2011. The work of GDP was partially supported by ERC under FP7, Advanced Grant no. 246923. The work of FM was partially supported by ERC under FP7, Starting Grant no. 258685 and Advanced Grant no. 226234, by the Institute for Computational Engineering and Sciences and by the Mathematics Department of the University of Texas at Austin during the time he was visiting these institutions, and by NSF Grant DMS-1265910. Publisher Copyright: {\textcopyright} European Mathematical Society 2017.",
year = "2017",
doi = "10.4171/JEMS/669",
language = "English (US)",
volume = "19",
pages = "395--439",
journal = "Journal of the European Mathematical Society",
issn = "1435-9855",
publisher = "European Mathematical Society Publishing House",
number = "2",
}