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A new proof of the affine isoperimetric inequality for Orlicz mean zonoids

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The Orlicz mean zonoid is defined by Guo, Leng and Du, and establish an affine isoperimetric inequality for it. Using shadow systems, we provide a new proof of the affine isoperimetric inequality for the Orlicz mean zonoids.

Abstract

The Orlicz mean zonoid is defined by Guo, Leng and Du, and establish an affine isoperimetric inequality for it. Using shadow systems, we provide a new proof of the affine isoperimetric inequality for the Orlicz mean zonoids.

참고문헌 (25)

  1. S. Campi, "On the reverse Lp-Busemann-Petty centroid inequality", Mathematika, 49, pp.1~11 (2002)
  2. S. Campi, "The Lp-Busemann-Petty centroid inequality", Adv. Math., 167, pp.128~141 (2002)
  3. S. Campi, "On volume product inequalities for convex sets", Proc. Amer. Math. Soc., 134, pp.2393~2402 (2006)
  4. F. W. Chen, "On the reverse Orlicz Busemann-Petty centroid inequality", Adv. in Appl. Math., 47, pp.820~828 (2011)
  5. L. J. Guo, "The Orlicz mean zonoid operator", J. Math. Anal. Appl., 424, pp.1261~1271 (2015)
  6. R.J. Gardner, "The Orlicz-Brunn-Minkowski theory: a general framework, additions, and inequalities", J. Differential Geom., 97, pp.427~476 (2014)
  7. C. Haberl, "General Lp affine isoperimetric inequalities", J. Differential Geom, 83, pp.1~26 (2009)
  8. C. Haberl, "Asymmetric affine Lp Sobolev inequalities", J. Funct. Anal., 257, pp.641~658 (2009)
  9. C. Haberl, "An asymmetric affine Póolya-Szegö principle", Math. Ann, 352, pp.517~542 (2012)
  10. C. Haberl, "The even Orlicz Minkowski problem", Adv. Math, 224, pp.2485~2510 (2010)
  11. C. Haberl, "The centro-affine Hadwiger theorem", J. Amer. Math. Soc, 27, pp.685~705 (2014)
  12. E. Lutwak, "Orlicz centroid bodies", J. Differential Geom., 84, pp.365~387 (2010)
  13. E. Lutwak, "Orlicz projection bodies", Adv. Math., 223, pp.220~242 (2010)
  14. M. Ludwig, "Minkowski valuations", Trans. Amer. Math. Soc., 357, pp.4191~4213 (2005)
  15. M. Ludwig, "A classification of SL(n)invariant valuations", Ann. of Math., 172, pp.1223~1271 (2010)
  16. A. J. Li, "A new proof of the Orlicz Busemann-Petty centroid inequality", Proceedings of The American Mathematical Society, 139(4), pp.1473~1481 (2011)
  17. L. Parapatits, "SL(n)-covariant Lp-Minkowski valuations", J. Lond. Math. Soc., 89, pp.397~414 (2014)
  18. L. Parapatits, "SL(n)-contravariant Lp-Minkowski valuations", Trans. Amer. Math. Soc., 366, pp.1195~1211 (2014)
  19. C. M. Petty, "Convexity and its applications", pp.264~276 (1983), Birkh auser
  20. C. A. Rogers, "Some extremal problems for convex bodies", Mathematika, 5, pp.93~102 (1958)
  21. G. C. Shephard, "Shadow system of convex sets", Israel J. Math., 2, pp.229~236 (1964)
  22. F. E. Schuster, "Volume inequalities for asymmetric Wulff shapes", J. Differential Geom., 92, pp.263~283 (2012)
  23. M. Weberndorfer, "Shadow systems of asymmetric Lp zonotopes", Adv. Math., 240, pp.613~635 (2013)
  24. G. T. Wang, "Volume inequalities for Orlicz zonotopes", J. Math. Anal. Appl., 391, pp.183~189 (2012)
  25. G. Zhang, "Restricted chord projection and affine inequalities", Geom. Dedicata, 39, pp.213~222 (1991)

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