Geodesic
Isoperimetric problem on the real line
Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part 13, Tome 216 (1994), pp. 5-9 
S. G. Bobkov. Isoperimetric problem on the real line. Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part 13, Tome 216 (1994), pp. 5-9. http://geodesic.mathdoc.fr/item/ZNSL_1994_216_a0/
@article{ZNSL_1994_216_a0,
     author = {S. G. Bobkov},
     title = {Isoperimetric problem on the real line},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--9},
     year = {1994},
     volume = {216},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1994_216_a0/}
}
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The isoperimetric problem on the real line for distributions with continuous positive densities is considered. Necessary and sufficient conditions under which the intervals $(-\infty,a)$ are extremal are suggested. Bibliography: 5 titles.