On isoperimetric sets of radially symmetric measures

Details On isoperimetric sets of radially symmetric measures On isoperimetric sets of radially symmetric measures

2010-02-09

arxiv.org/abs/1002.1829v4

Mathematics

Probability

30 pages, 13 figures, 28 references; minor changes

Scientific paper

We study the isoperimetric problem for the radially symmetric measures. Applying the spherical symmetrization procedure and variational arguments we reduce this problem to a one-dimensional ODE of the second order. Solving numerically this ODE we get an empirical description of isoperimetric regions of the planar radially symmetric exponential power laws. We also prove some isoperimetric inequalities for the log-convex measures. We show, in particular, that the symmetric balls of large size are isoperimetric sets for strictly log-convex and radially symmetric measures. In addition, we establish some comparison results for general log-convex measures.

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