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Journal of Mathematical Sciences

, Volume 88, Issue 1, pp 3–6 | Cite as

Isoperimetric problem on the real line

  • S. G. Bobkov
Article

Abstract

The isoperimetric problem on the real line for distributions with continuous positive densities is considered. Necessary and sufficient conditions under which the intervals (−∞, a) are extremal are suggested. Bibliography: 5 titles.

Keywords

Real Line Positive Density Isoperimetric Problem Continuous Positive Density 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    V. N. Sudakov and B. S. Tsirel'son, “Extremal properties of half-spaces for spherically invariant measures,”J. Sov. Math.,9, 9–18 (1978).CrossRefGoogle Scholar
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    C. Borell, “The Brunn-Minkowski inequality in Gauss space,”Invent. Math.,30, 207–216 (1975).CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    M. Talagrand, “A new isoperimetric inequality and the concentration of measure phenomenon,”Lect. Notes Math.,1469, 94–124 (1989–1990).MathSciNetGoogle Scholar
  4. 4.
    S. Bobkov, “Isoperimetric problem for uniform enlargement,” Univ. of North Carolina at Chapel Hill, Dept. of Statistics. Tech. Report No. 394 (1993).Google Scholar
  5. 5.
    S. Bobkov, “Extremal properties of half-spaces for log-concave distributions,” Univ. of North Carolina at Chapel Hill, Dept. of Statistics. Tech. Report No. 396 (1993).Google Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • S. G. Bobkov

There are no affiliations available

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