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Isoperimetric problem for uniform enlargement

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EN
We consider an isoperimetric problem for product measures with respect to the uniform enlargement of sets. As an example, we find (asymptotically) extremal sets for the infinite product of the exponential measure.
Twórcy
autor
  • Department of Mathematics, Syktyvkar University, 167001 Syktyvkar, Russia , bobkov@mathematik.uni.bielefeld.de,
  • Fakultät für Mathematik, Universität Bielefeld, 33501 Bielefeld, Deutschland
Bibliografia
  • [AM] D. Amir and V. D. Milman, Unconditional and symmetric sets in n-dimensional normed spaces, Israel J. Math. 37 (1980), 3-20.
  • [B1] S. G. Bobkov, Isoperimetric problem for uniform enlargement, Center for Stochastic Processes, Dept. of Statistics, Univ. of North Carolina at Chapel Hill, Tech. Report 394 (1993).
  • [B2] S. G. Bobkov, Extremal properties of half-spaces for log-concave distributions, Ann. Probab. 24 (1996), 35-48.
  • [B3] S. G. Bobkov, A functional form of the isoperimetric inequality for the Gaussian measure, J. Funct. Anal. 135 (1996), 39-49.
  • [B4] S. G. Bobkov, Isoperimetric inequalities for distributions of exponential type, Ann. Probab. 22 (1994), 978-994.
  • [BH1] S. G. Bobkov and C. Houdré, A characterization of Gaussian measures via the isoperimetric property of half-spaces, Zap. Nauch. Semin. SPOMI RAN 228 (1996), 31-38 (in Russian); English transl.: J. Math. Sci., to appear.
  • [BH2] S. G. Bobkov and C. Houdré, Some connections between Sobolev-type inequalities and isoperimetry, Mem. Amer. Math. Soc., to appear.
  • [BH3] S. G. Bobkov and C. Houdré, Isoperimetric constants for product probability measures, Ann. Probab., to appear.
  • [Bor] C. Borell, The Brunn-Minkowski inequality in Gauss space, Invent. Math. 30 (1975), 207-211.
  • [BZ] Yu. D. Burago and V. A. Zalgaller, Geometric Inequalities, Springer, 1988; transl. from the Russian edition, Nauka, Moscow, 1980.
  • [H] L. H. Harper, Optimal numbering and isoperimetric problems on graphs, J. Combin. Theor. 1 (1966), 385-393.
  • [Led] M. Ledoux, Isoperimetry and Gaussian analysis, in: Ecole d'été de Probabilités de Saint-Flour, 1994, Lecture Notes in Math., Springer, to appear.
  • [Lev] P. Lévy, Problèmes concrets d'analyse fonctionnelle, Gauthier-Villars, Paris, 1951.
  • [Sch] E. Schmidt, Die Brunn-Minkowskische Ungleichung und ihr Spiegelbild sowie die isoperimetrische Eigenschaft der Kugel in der euklidischen und nichteuklidischen Geometrie I, II, Math. Nachr. 1 (1948), 81-157; 2 (1949), 171-244.
  • [ST] V. N. Sudakov and B. S. Tsirel'son, Extremal properties of half-spaces for spherically invariant measures, J. Soviet Math. 9 (1978), 9-18; transl. from Zap. Nauchn. Sem. LOMI 41 (1974), 14-24 (in Russian).
  • [Tal1] M. Talagrand, An isoperimetric theorem on the cube and the Khinchine-Kahane inequalities, Proc. Amer. Math. Soc. 104 (1988), 905-909.
  • [Tal2] M. Talagrand, A new isoperimetric inequality and the concentration of measure phenomenon, in: Lecture Notes in Math. 1469, Springer, 1991, 94-124.
  • [Tal3] M. Talagrand, Concentration of measure and isoperimetric inequalities in product spaces, Publ. Math. IHES 81 (1995), 73-205.
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Bibliografia
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