EDP Sciences logo
Submit your paper
Search
Menu
All issues Volume 27 / No 1 (March 2022) Wuhan Univ. J. Nat. Sci., 27 1 (2022) 42-48 References
Open Access
Issue
Wuhan Univ. J. Nat. Sci.
Volume 27, Number 1, March 2022
Page(s) 42 - 48
DOI https://doi.org/10.1051/wujns/2022271042
Published online 16 March 2022
  1. Bernig A. Centroid bodies and the convexity of area functionals [J]. The Journal of Differential Geometry, 2014, 98(3): 357-373. [Google Scholar]
  2. Chen F, Yang C. A new proof of the Orlicz-Lorentz centroid inequality [J]. Journal of Inequalities and Applications, 2019, 2019(1): 1-12. [CrossRef] [PubMed] [Google Scholar]
  3. Lutwak E. On some affine isoperimetric inequalities [J]. The Journal of Differential Geometry, 1986, 23(1):1-13. [Google Scholar]
  4. Lutwak E. Centroid bodies and dual mixed volumes [J]. Proceedings of the London Mathematical Society, 1990, 60(2): 365-391. [CrossRef] [Google Scholar]
  5. Lutwak E, Yang D, Zhang G Y. The Cramer-Rao inequality for star bodies [J]. Duke Mathematical Journal, 2002, 112(1): 59-81. [MathSciNet] [Google Scholar]
  6. Lutwak E, Yang D, Zhang G Y. Orlicz centroid bodies [J]. The Journal of Differential Geometry, 2010, 84(2): 365-387. [Google Scholar]
  7. Petty C M. Centroid surfaces [J]. Pacific Journal of Mathematics, 1961, 11(3):1535-1547. [CrossRef] [MathSciNet] [Google Scholar]
  8. Shi K J, Wang Y. The asymmetric version of generalized centroid bodies [J]. Communication on Applied Mathematics and Computation, 2018, 32(3): 425-436. [MathSciNet] [Google Scholar]
  9. Xiong G, Xu D. Orlicz centroid bodies of ellipsoids [J]. Communication on Applied Mathematics & Computation, 2012, 26(1): 365-388. [Google Scholar]
  10. Yu W Y, Wu D H. The monotony properties of generalized projection bodies, intersection bodies and centroid bodies [J]. Journal of the Korean Mathematical Society, 2006, 43: 609-622. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  11. Zhu G X. The Orlicz centroid inequality for star bodies [J]. Advances in Applied Mathematics, 2012, 48(2): 432-445. [CrossRef] [MathSciNet] [Google Scholar]
  12. Lutwak E, Zhang G Y. Blaschke-Santalӧ inequalities [J]. The Journal of Differential Geometry, 1997, 47(1): 1-16. [Google Scholar]
  13. Feng Y B, Wang W D. The Shephard type problems and monotonicity for Lp-mixed centroid bodies [J]. Indian Journal of Pure & Applied Mathematics, 2014, 45(3): 265-284. [CrossRef] [MathSciNet] [Google Scholar]
  14. Feng Y B, Wang W D. Shephard type problems for Lp centroid bodies [J]. Mathematical Inequalities & Applications, 2014, 17(3): 865-877. [MathSciNet] [Google Scholar]
  15. Feng Y B, Wang W D, Lu F H. Some inequalities on general Lp centroid bodies [J]. Mathematical Inequalities & Applications, 2015, 18(1):39-49. [NASA ADS] [MathSciNet] [Google Scholar]
  16. Milman E. On the mean-width of isotropic convex bodies and their associated Lp-centroid bodies [J]. International Mathematics Research Notices, 2015: 3408-3423. [Google Scholar]
  17. Pei Y N, Wang W D. Shephard type problems for general Lp-centroid bodies [J]. Journal of Inequalities & Applications, 2015, 2015(1): 287. [CrossRef] [Google Scholar]
  18. Wang W D, Lu F H, Leng G S. A type of monotonicity on the Lp centroid body and Lp projection body [J]. Mathematical Inequalities & Applications, 2005, 8(4): 735-742. [CrossRef] [MathSciNet] [Google Scholar]
  19. Wang W D, Leng G S. Inequalities of the quermassintegrals for the Lp-projection bodys and the Lp-centroid body [J]. Acta Mathematica Scientia, Series B, English Edition, 2010, 30(1): 359-368. [Google Scholar]
  20. Wang W D, Leng G S. Monotonicity of Lp-centroid body [J]. Journal of Systems Science and Mathematical Sciences, 2008, 28(2): 154-162. [Google Scholar]
  21. Yuan J, Zhao L Z, Leng G S. Inequalities for centroid body [J]. Taiwanese Journal of Mathematics, 2007, 11(5): 1315-1325. [Google Scholar]
  22. Grinberg E, Zhang G Y. Convolutions, transforms, and convex bodies [J]. Proceedings of the London Mathematical Society, 1999, 78(1): 77-115. [CrossRef] [MathSciNet] [Google Scholar]
  23. Abardia J, Bernig A. Projection bodies in complex vector spaces [J]. Advances in Mathematics, 2012, 227(2): 830-846. [Google Scholar]
  24. Abardia J. Difference bodies in complex vector spaces [J]. Journal of Functional Analysis, 2012, 263(11): 3588-3603. [CrossRef] [MathSciNet] [Google Scholar]
  25. Koldobsky A, Paouris G, Zymonopoulou M. Complex intersection bodies [J]. Journal of the London Mathematical Society, Second Series, 2013, 88(2): 538-562. [Google Scholar]
  26. Liu L J, Wang W, Huang Q Z. On polars of mixed complex projection bodies [J]. Bulletin of the Korean Mathematical Society, 2005, 52(2): 453-465. [Google Scholar]
  27. Li C, Wang W D. Inequalities for complex centroid bodies [J]. Acta Mathematica Hungarica, 2020, 161: 313-326. [CrossRef] [MathSciNet] [Google Scholar]
  28. Wang W, Liu L J. Complex Lp affine isoperimetric inequalities [J]. Advances in Applied Mathematics, 2021, 122: 102108. [CrossRef] [Google Scholar]
  29. Haberl C. Complex affine isoperimetric inequalities [J]. Calculus of Variations and Partial Differential Equations, 2019, 58(5): 169. [CrossRef] [Google Scholar]
  30. Wu Y C. On complex affine isoperimetric inequalities [J]. Mathematical Inequalities & Applications, 2021, 24(3): 655-678. [MathSciNet] [Google Scholar]
  31. Gardner R J. Geometric Tomography [M]. 2nd Edition. Cambridge: Cambridge University Press, 2006. [CrossRef] [Google Scholar]
  32. Schneider R. Convex Bodies: The Brunn-Minkowski Theory [M]. 2nd Edition. Cambridge: Cambridge University Press, 2014. [Google Scholar]
  33. Lutwak E. The Brunn-Minkowski-Firey theory I: Mixed volumes and the Minkowski problem [J]. The Journal of Differential Geometry, 1993, 38(1): 131-150. [Google Scholar]
  34. Lutwak E. The Brunn-Minkowski-Firey theory II: Affine and geominimal surface areas [J]. Advances in Mathematics, 1996, 118(1): 244-294. [CrossRef] [MathSciNet] [Google Scholar]
  35. Hardy G H, Littlewood J E, Pólya G. Inequalities [J]. Bulletin of the American Mathematical Society, 1953, 59: 411-412. [CrossRef] [MathSciNet] [Google Scholar]
  36. Lu F H, Leng G S. On Lp-Brunn-Minkowski type inequalities of convex bodies [J]. Boletín de la Sociedad Matemática Mexicana, Third Series, 2007, 13(1): 167-176. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.