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A stability result for p-centroid bodies

LuJun Guo|Gangsong Leng|Youjiang Lin
대한수학회 (The Korean Mathematical Society)|2018.01|대한수학회보 (Bulletin of the KMS)|제55권 제1호|pp. 139-148

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키워드

convex body$p$-centroid bodyspherical integral transformation$p$-cosine transformation
주제분류수학

초록

In this paper, we prove a stability result for $p$-centroid bodies with respect to the Hausdorff distance. As its application, we show that the symmetric convex body is determined by its $p$-centroid body.

Abstract

In this paper, we prove a stability result for $p$-centroid bodies with respect to the Hausdorff distance. As its application, we show that the symmetric convex body is determined by its $p$-centroid body.

참고문헌 (27)

  1. S. Campi, "The <TEX>$L^p$<", TEX>-Busemann-Petty centroid inequlity, 2002, pp.167, 128~141
  2. S. Campi, "On the reverse <TEX>$L_p$<", TEX>-Busemann-Petty centroid inequality, 2002, pp.49(1-2), 1~11
  3. I. Fary, "Der zentralsymmetrische Kern und die zentralsymmetrische Hulle von konvexen Korpern", Math. Ann., 122, pp.205~220 (1950)[DOI]
  4. B. Fleury, "A stability result for mean width of <TEX>$L_p$<", TEX>-centroid bodies, 2007, pp.214(2), 865~877
  5. R. J. Gardner, "P-cross-section bodies", Indiana Univ. Math. J., 48(2), pp.593~613 (1999)
  6. H. Groemer, "Geometric Applications of Fourier Series and Spherical Harmonics" (1996), Cam-bridge University Press
  7. P. M. Gruber, "Convex and Discrete Geometry", Grundlehren Math. Wiss., 336 (2007)
  8. L. Guo, "Determination of star bodies from p-centroid bodies", Proc. Indian Acad. Sci. Math. Sci., 123(4), pp.577~586 (2013)[DOI]
  9. L. Guo, "Stable determination of convex bodies from centroid bodies", Houston J. Math., 40(2), pp.395~406 (2014)
  10. A. Koldobsky, "Common subspaces of <TEX>$L_p$<", TEX>-spaces, 1994, pp.122(1), 207~212
  11. E. Lutwak, "On some affine isoperimetric inequalities", J. Differential Geom., 23(1), pp.1~13 (1986)[DOI]
  12. E. Lutwak, "Centroid bodies and dual mixed volumes", Proc. London Math. Soc., 60(2), pp.365~391 (1990)
  13. E. Lutwak, "The Brunn-Minkowski-Firey theory I: Mixed volumes and the Minkowski problem", J. Differential Geom., 38(1), pp.131~150 (1993)[DOI]
  14. E. Lutwak, "The Brunn-Minkowski-Firey theory II: Affine and geominimal surface areas", Adv. Math., 118(2), pp.244~294 (1996)[DOI]
  15. E. Lutwak, "<TEX>$L_p$<", TEX> affine isoperimetric inequalities, 2000, pp.56(1), 111~132
  16. E. Lutwak, "Sharp affine <TEX>$L_p$<", TEX> Sobolev inequalities, 2002, pp.62(1), 17~38
  17. E. Lutwak, "Orlicz centroid bodies", J. Differential Geom., 84(2), pp.365~387 (2010)[DOI]
  18. E. Lutwak, "Blaschke-Santalo inequalities", J. Differential Geom., 47(1), pp.1~16 (1997)[DOI]
  19. V. D. Milman, "Isotropic position and inertia ellipsoid and zonoids of the unit ball of a normed n-dimensional space, Geometric aspects of functional analysis (19878)", Lecture Notes in Math., 1376, pp.64~104 (1989)
  20. G. Paouris, "Concentration of mass on isotropic convex bodies", C. R. Math. Acad. Sci. Paris, 342(3), pp.179~182 (2006)[DOI]
  21. G. Paouris, "Small ball probability estimates for log-concave measures", Trans. Amer. Math. Soc., 364(1), pp.287~308 (2012)[DOI]
  22. C. M. Petty, "Centroid surfaces", Pacific J. Math., 11, pp.1535~1547 (1961)[DOI]
  23. R. Schneider, "Convex bodies: The Brunn-Minkowski Theory, Encyclopedia of Mathe-matics and its Applications, Vol. 44" (1993), Cambridge University Press
  24. G. Zhang, "Centered bodies and dual mixed volumes", Trans. Amer. Math. Soc., 345(2), pp.777~801 (1994)[DOI]
  25. G. Zhu, "The Orlicz centroid inequality for star bodies", Adv. Appl. Math., 48(2), pp.432~445 (2012)[DOI]
  26. G. Zhu, "The logarithmic Minkowski problem for polytopes", Adv. Math., 262, pp.909~931 (2014)[DOI]
  27. G. Zhu, "The centro-affine Minkowski problem for polytopes", J. Differential Geom., 101(1), pp.159~174 (2015)[DOI]

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