EDP Sciences logo
Submit your paper
Search
Menu
All issues Volume 30 / No 5 (October 2025) Wuhan Univ. J. Nat. Sci., 30 5 (2025) 471-478 References
Open Access
Issue
Wuhan Univ. J. Nat. Sci.
Volume 30, Number 5, October 2025
Page(s) 471 - 478
DOI https://doi.org/10.1051/wujns/2025305471
Published online 04 November 2025
  1. Aleksandrov A. On the theory of mixed volumes of convex bodies. III. Extension of two theorems of Minkowski on convex polyhedra to arbitrary convex bodies[J]. Mathematics of the Ussr Sbornik, 1938, 3: 27-46. [Google Scholar]
  2. Aleksandrov A. On the surface area measure of convex body[J]. Mathematics of the Ussr Sbornik, 1939, 6: 167-174. [Google Scholar]
  3. Andrews B. Gauss curvature flow: The fate of the rolling stones[J]. Inventiones Mathematicae, 1999, 138(1): 151-161. [Google Scholar]
  4. Böröczky K J, Lutwak E, Yang D, et al. The logarithmic Minkowski problem[J]. Journal of the American Mathematical Society, 2013, 26(3): 831-852. [Google Scholar]
  5. Chen W X. Formula Minkowski problem with not necessarily positive data[J]. Advances in Mathematics, 2006, 201(1): 77-89. [Google Scholar]
  6. Chou K S, Wang X J. The Formula -Minkowski problem and the Minkowski problem in centroaffine geometry[J]. Advances in Mathematics, 2006, 205(1): 33-83. [Google Scholar]
  7. Evans L C. Measure Theory and Fine Properties of Functions[M]. London: Routledge, 2018. [Google Scholar]
  8. Lutwak E. The Brunn-Minkowski-Firey theory. I. Mixed volumes and the Minkowski problem[J]. Journal of Differential Geometry, 1993, 38(1): 131-150. [Google Scholar]
  9. Lutwak E. The Brunn-Minkowski-Firey theory II: Affine and geominimal surface areas[J]. Advances in Mathematics, 1996, 118(2): 244-294. [CrossRef] [MathSciNet] [Google Scholar]
  10. Lutwak E, Yang D, Zhang G Y. On the Formula -Minkowski problem[J]. Transactions of the American Mathematical Society, 2004, 356(11): 4359-4370. [Google Scholar]
  11. Minkowski H. Allgemeine Lehrsätze über die konvexen polyeder[J]. Ausgewählte Arbeitenzur Zahlentheorie und zur Geometrie: Mit D Hilberts Gedächtnisrede auf H Minkowski, Göttingen, 1909, 1989: 121-139. [Google Scholar]
  12. Zhu G. The Formula Minkowski problem for polytopes for Formula [J]. Journal of Functional Analysis, 2015, 269(4): 1070-1094. [Google Scholar]
  13. Zhu G X. The logarithmic Minkowski problem for polytopes[J]. Advances in Mathematics, 2014, 262: 909-931. [Google Scholar]
  14. Zhu G. The Formula Minkowski problem for polytopes for Formula [J]. Indiana University Mathematics Journal, 2017, 66: 1333-1350. [Google Scholar]
  15. Tang L Z, Wang W. A characterization of the polarity mapping for convex bodies[J]. Wuhan University Journal of Natural Sciences, 2023, 28(2): 93-98. [Google Scholar]
  16. Lin Y J. The reverse petty projection inequality[J]. Wuhan University Journal of Natural Sciences, 2019, 24(4): 290-294. [Google Scholar]
  17. Wei X N, Lin Y J. Security Steiner's inequality on layering functions[J]. Wuhan University Journal of Natural Sciences, 2022, 27(2): 125-127. [Google Scholar]
  18. Zhang X F, Wu S H. New Brunn-Minkowski type inequalities for general width-integral of index i[J]. Wuhan University Journal of Natural Sciences, 2019, 24(6): 474-478. [Google Scholar]
  19. Chen Z M. The Lp Minkowski problem for q-capacity[J]. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2021, 151(4): 1247-1277. [Google Scholar]
  20. Colesanti A, Cuoghi P. The Brunn-Minkowski inequality for the Formula -dimensional logarithmic capacity of convex bodies[J]. Potential Analysis, 2005, 22: 289-304. [Google Scholar]
  21. Colesanti A, Nystr¨om K, Salani P, et al. The Hadamard variational formula and the Minkowski problem for Formula -capacity[J]. Advances in Mathematics, 2015, 285: 1511-1588. [Google Scholar]
  22. Colesanti A, Salani P. The Brunn-Minkowski inequality for p-capacity of convex bodies[J]. Mathematische Annalen, 2003, 327(3): 459-479. [Google Scholar]
  23. Feng Y B, Zhou Y P, He B W. The Formula electrostatic q-capacitary Minkowski problem for general measures[J]. Journal of Mathematical Analysis and Applications, 2020, 487(1): 123959. [Google Scholar]
  24. Lu X B, Xiong G. The Formula Minkowski problem for the electrostatic Formula -capacity for Formula [J]. Indiana University Mathematics Journal, 2021, 70(5): 1869-1901. [Google Scholar]
  25. Wang W, He R G. The discrete logarithmic Minkowski problem for q-capacity[J]. Journal of Mathematical Analysis and Applications, 2022, 511(2): 126101. [Google Scholar]
  26. Xiong G, Xiong J W, Xu L. The Formula capacitary Minkowski problem for polytopes[J]. Journal of Functional Analysis, 2019, 277(9): 3131-3155. [Google Scholar]
  27. Xiao J. On the variational Formula -capacity problem in the plane[J]. Communications on Pure and Applied Analysis, 2015, 14(3): 959-968. [Google Scholar]
  28. Du Z, Xiong G. The Formula Minkowski problem for the electrostatic Formula -capacity[J]. Journal of Differential Geometry, 2020, 116(3): 555-596. [Google Scholar]
  29. Liu L J. Complex-valued valuations on Formula spaces[J]. Wuhan University Journal of Natural Sciences, 27(1): 35-41. [Google Scholar]
  30. Wei B, Wang W D. Some inequalities for the Formula -mixed quermassintegrals[J]. Wuhan University Journal of Natural Sciences, 2013, 18(3): 233-236. [Google Scholar]
  31. Wang W D. On reverses of the Formula -Busemann-Petty centroid inequality and its applications[J]. Wuhan University Journal of Natural Sciences, 2010, 15(4): 292-296. [Google Scholar]
  32. Ma J Y, Yang W J, Zhou Y P. Some inequalities about the general Formula -mixed width-integral of convex bodies[J]. Wuhan University Journal of Natural Sciences, 2022, 27(4): 281-286. [Google Scholar]
  33. Aikawwa H, Essen M. Potential Theory-Selected Topics[M]. Berlin: Springer-Verlag, 1996. [Google Scholar]
  34. Jerison D. A Minkowski problem for electrostatic capacity[J]. Acta Mathematica, 1996, 176(1): 1-47. [Google Scholar]
  35. Saff E, Totik V. Logarithmic Potentials with External Fields[M]. Berlin: Springer Science and Business Media, 2013. [Google Scholar]
  36. Xiong G, Xiong J W. The logarithmic capacitary Minkowski problem for polytopes[J]. Acta Mathematica Sinica, English Series, 2022, 38(2): 406-418. [Google Scholar]
  37. Betsakos D. Geometric versions of Schwarzs lemma for quasiregular mappings[J]. Proceedings of the American Mathematical Society, 2011, 139(4): 1397-1407. [Google Scholar]
  38. Caffarelli L A. Interior W 2,p-estimates for solutions of the Monge-Ampère equation[J]. Annals of Mathematics, 1990, 131(1): 135-150. [Google Scholar]
  39. Caffarelli L A, Jerison D, Lieb E H. On the case of equality in the Brunn-Minkowski inequality for capacity[C]//Inequalities. Berlin: Springer-Verlag, 2002: 497-511. [Google Scholar]
  40. Caffarelli L A. Some regularity properties of solution of Monge-Ampère equation[J]. Commun Pure Appl Math, 1991, 44: 965-969. [Google Scholar]
  41. Akman M, Gong J, Hineman J, et al. The Brunn-Minkowski Inequality and a Minkowski Problem for Nonliner Capacity[M]. New York: American Mathematical Society, 2022. [Google Scholar]
  42. Firey W J. Formula -means of convex bodies[J]. Mathematica Scandinavica, 1962, 10: 17-24. [Google Scholar]
  43. Akman M, Lewis J, Saari O, et al. The Brunn-Minkowski inequality and a Minkowski problem for Formula -harmonic Green's function[J]. Advances in Calculus of Variations, 2021, 14(2): 247-302. [Google Scholar]
  44. Xiao J. Geometrical logarithmic capacitance[J]. Advances in Mathematics, 2020, 365: 107048. [Google Scholar]
  45. Gardner R J, Hug D, Weil W. Operations between sets in geometry[J]. Journal of the European Mathematical Society, 2013, 15(6): 2297-2352. [Google Scholar]
  46. Xi D M, Jin H L, Leng G S. The Orlicz Brunn-Minkowski inequality[J]. Advances in Mathematics, 2014, 260: 350-374. [Google Scholar]
  47. Lutwak E, Yang D, Zhang G Y. Orlicz projection bodies[J]. Advances in Mathematics, 2010, 223(1): 220-242. [CrossRef] [MathSciNet] [Google Scholar]
  48. Lutwak E, Yang D, Zhang G Y. Orlicz centroid bodies[J]. Journal of Differential Geometry, 2010, 84(2): 365-387. [Google Scholar]
  49. Böröczky K J. Stronger versions of the Orlicz-Petty projection inequality[J]. Journal of Differential Geometry, 2013, 95(2): 215-247. [Google Scholar]
  50. Haberl C, Lutwak E, Yang D, et al. The even Orlicz Minkowski problem[J]. Advances in Mathematics, 2010, 224(6): 2485-2510. [Google Scholar]
  51. Ludwig M. General affine surface areas[J]. Advances in Mathematics, 2010, 224(6): 2346-2360. [Google Scholar]
  52. Ye D P. On the monotone properties of general affine surfaces under the Steiner symmetrization[J]. Indiana University Mathematics Journal, 2014, 63(1): 5205. [Google Scholar]
  53. Zou D, Xiong G. Orlicz-John ellipsoids[J]. Advances in Mathematics, 2014, 265: 132-168. [Google Scholar]
  54. Wang W, Liu L J. Orlicz-Brunn-Minkowski inequalities for complex projection bodies[J]. Wuhan University Journal of Natural Sciences, 2021, 26(1): 8-14. [Google Scholar]
  55. Hong H, Ye D P, Zhang N. The Formula -capacitary Orlicz-Hadamard variational formula and Orlicz- Minkowski problems[J]. Calculus of Variations and Partial Differential Equations, 2018, 57: 1-31. [Google Scholar]
  56. Ji L, Yang Z. The discrete Orlicz-Minkowski problem for Formula -capacity[J]. Acta Mathematica Scientia, English Series, 2022, 42: 1403-1413. [Google Scholar]
  57. Xiong G, Xiong J W. The Orlicz Minkowski problem for the electrostatic Formula -capacity[J]. Advances in Applied Mathematics, 2022, 137: 102339. [Google Scholar]
  58. Hu Z J, Li H. On the Orlicz Minkowski problem for logarithmic capacity[J]. Journal of Mathematical Analysis and Applications, 2022, 510(1): 126005. [Google Scholar]
  59. Gardner R M. Geometric Tomography[M].Second Edition. Cambridge: Cambridge University Press, 2006. [Google Scholar]
  60. Gruber P M. Convex and Discrete Geometry[M]. Berlin: Springer-Verlag, 2007. [Google Scholar]
  61. Schneider R. Convex Bodies: The Brunn-Minkowski Theory[M]. Second Expanded Edition. Cambridge: Cambridge University Press, 2014. [Google Scholar]
  62. Xiao J. Exploiting log-capacity in convex geometry[J]. Asian Journal of Mathematics, 2018, 22(5): 955-980. [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.