Some Connections between Isoperimetric and Sobolev-type Inequalities - Bobkov, Serguei / Houdré, Christian
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For Borel probability measures on metric spaces, the authors study the interplay between isoperimetric and Sobolev-type inequalities. In particular the question of finding optimal constants via isoperimetric quantities is explored. Also given are necessary and sufficient conditions for the equivalence between the extremality of some sets in the ispperimetric problem and the validity of some analytic inequalities. Much attention is devoted to probability distributions on the real line, the normalized Lebesgue measure on the Euclidean sheres, and the canonical Gaussian measure on the Euclidean space.…mehr

Produktbeschreibung
For Borel probability measures on metric spaces, the authors study the interplay between isoperimetric and Sobolev-type inequalities. In particular the question of finding optimal constants via isoperimetric quantities is explored. Also given are necessary and sufficient conditions for the equivalence between the extremality of some sets in the ispperimetric problem and the validity of some analytic inequalities. Much attention is devoted to probability distributions on the real line, the normalized Lebesgue measure on the Euclidean sheres, and the canonical Gaussian measure on the Euclidean space.