Geodesic
Characterization of Gaussian measures by the isoperimetric property of half-spaces
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 1, Tome 228 (1996), pp. 31-38

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If the half-spaces of the form $\{x\in\mathbb R^n\colon x_1\le c\}$ are extremal in the isoperimetric problem for the product-measure $\mu^n$, $n\ge2$, then the marginal distribution $\mu$ is Gaussian. Bibl. 8 titles. 
@article{ZNSL_1996_228_a3,
     author = {S. G. Bobkov and C. Houdr\'e},
     title = {Characterization of {Gaussian} measures by the isoperimetric property of half-spaces},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {31--38},
     publisher = {mathdoc},
     volume = {228},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1996_228_a3/}
}
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S. G. Bobkov; C. Houdré. Characterization of Gaussian measures by the isoperimetric property of half-spaces. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 1, Tome 228 (1996), pp. 31-38. http://geodesic.mathdoc.fr/item/ZNSL_1996_228_a3/