Inequalities for general width-integrals of Blaschke-Minkowski homomorphisms

Chao Li; Weidong Wang

Czechoslovak Mathematical Journal (2020)

  • Volume: 70, Issue: 3, page 767-779
  • ISSN: 0011-4642

Abstract

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We establish some inequalities for general width-integrals of Blaschke-Minkowski homomorphisms. As applications, inequalities for width-integrals of projection bodies are derived.

How to cite

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Li, Chao, and Wang, Weidong. "Inequalities for general width-integrals of Blaschke-Minkowski homomorphisms." Czechoslovak Mathematical Journal 70.3 (2020): 767-779. <http://eudml.org/doc/297304>.

@article{Li2020,
abstract = {We establish some inequalities for general width-integrals of Blaschke-Minkowski homomorphisms. As applications, inequalities for width-integrals of projection bodies are derived.},
author = {Li, Chao, Wang, Weidong},
journal = {Czechoslovak Mathematical Journal},
keywords = {general width-integral; volume difference type inequality; Blaschke-Minkowski homomorphism; Brunn-Minkowski type inequality; projection body},
language = {eng},
number = {3},
pages = {767-779},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Inequalities for general width-integrals of Blaschke-Minkowski homomorphisms},
url = {http://eudml.org/doc/297304},
volume = {70},
year = {2020},
}

TY - JOUR
AU - Li, Chao
AU - Wang, Weidong
TI - Inequalities for general width-integrals of Blaschke-Minkowski homomorphisms
JO - Czechoslovak Mathematical Journal
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 70
IS - 3
SP - 767
EP - 779
AB - We establish some inequalities for general width-integrals of Blaschke-Minkowski homomorphisms. As applications, inequalities for width-integrals of projection bodies are derived.
LA - eng
KW - general width-integral; volume difference type inequality; Blaschke-Minkowski homomorphism; Brunn-Minkowski type inequality; projection body
UR - http://eudml.org/doc/297304
ER -

References

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  1. Beckenbach, E., Bellman, R., 10.1007/978-3-642-64971-4, Ergebnisse der Mathematik und Ihrer Grenzgebiete 30, Springer, New York (1965). (1965) Zbl0126.28002MR0192009DOI10.1007/978-3-642-64971-4
  2. Berg, A., Parapatits, L., Schuster, F. E., Weberndorfer, M., 10.1090/tran/7434, Trans. Am. Math. Soc. 370 (2018), 5245-5277. (2018) Zbl1390.52024MR3787383DOI10.1090/tran/7434
  3. Blaschke, W., Vorlesungen über Integralgeometrie, German VEB Deutscher Verlag der Wissenschaften, Berlin (1955). (1955) Zbl0066.40703MR0076373
  4. Cheung, W.-S., Zhao, C.-J., 10.15352/bjma/1240336275, Banach J. Math. Anal. 2 (2008), 70-77. (2008) Zbl1155.52005MR2404711DOI10.15352/bjma/1240336275
  5. Dresher, M., 10.1215/s0012-7094-53-02026-2, Duke Math. J. 20 (1953), 261-271. (1953) Zbl0050.28202MR0055389DOI10.1215/s0012-7094-53-02026-2
  6. Feng, Y., 10.22436/jnsa.009.06.64, J. Nonlinear Sci. Appl. 9 (2016), 4226-4234. (2016) Zbl1347.52004MR3530126DOI10.22436/jnsa.009.06.64
  7. Feng, Y., Wang, W., 10.5486/PMD.2014.5903, Publ. Math. 85 (2014), 297-308. (2014) Zbl1340.52006MR3291832DOI10.5486/PMD.2014.5903
  8. Feng, Y., Wang, W., Yuan, J., 10.5556/j.tkjm.46.2015.1689, Tamkang J. Math. 46 (2015), 217-227. (2015) Zbl1338.52005MR3406352DOI10.5556/j.tkjm.46.2015.1689
  9. Feng, Y., Wu, S., Brunn-Minkowski type inequalies for width-integrals of index i , J. Comput. Anal. Appl. 24 (2018), 1408-1418. (2018) MR3753402
  10. Feng, Y., Wu, S., Wang, W., 10.1216/RMJ-2017-47-8-2627, Rocky Mt. J. Math. 47 (2017), 2627-2640. (2017) Zbl1385.52005MR3760310DOI10.1216/RMJ-2017-47-8-2627
  11. Firey, W. J., 10.2140/pjm.1961.11.1263, Pac. J. Math. 11 (1961), 1263-1266. (1961) Zbl0122.41101MR0140003DOI10.2140/pjm.1961.11.1263
  12. Gardner, R. J., 10.1017/CBO9781107341029, Encyclopedia of Mathematics and Its Applications 58, Cambridge University Press, Cambridge (2006). (2006) Zbl1102.52002MR2251886DOI10.1017/CBO9781107341029
  13. Haberl, C., 10.4171/JEMS/341, J. Eur. Math. Soc. (JEMS) 14 (2012), 1565-1597. (2012) Zbl1270.52018MR2966660DOI10.4171/JEMS/341
  14. Cifre, M. A. Hernández, Nicolás, J. Yepes, 10.1007/s12220-014-9541-y, J. Geom. Anal. 26 (2016), 143-155. (2016) Zbl1339.52007MR3441506DOI10.1007/s12220-014-9541-y
  15. Ji, L., Zeng, Z., 10.21136/CMJ.2017.0180-16, Czech. Math. J. 67 (2017), 779-793. (2017) Zbl06770130MR3697916DOI10.21136/CMJ.2017.0180-16
  16. Li, Y., Wang, W., 10.1186/1029-242X-2014-131, J. Inequal. Appl. 2014 (2014), Article ID 131, 10 pages. (2014) Zbl1310.52003MR3253878DOI10.1186/1029-242X-2014-131
  17. Li, X.-Y., Zhao, C.-J., 10.7153/mia-17-33, Math. Inequal. Appl. 17 (2014), 443-450. (2014) Zbl1296.52004MR3235022DOI10.7153/mia-17-33
  18. Lu, F., Leng, G., On inequalities for i th width-integrals of convex bodies, Math. Appl. 19 (2006), 632-636 Chinese. (2006) Zbl1101.52001MR2254976
  19. Ludwig, M., 10.1090/S0002-9947-04-03666-9, Trans. Am. Math. Soc. 357 (2005), 4191-4213. (2005) Zbl1077.52005MR2159706DOI10.1090/S0002-9947-04-03666-9
  20. Lutwak, E., 10.1090/S0002-9939-1975-0383254-5, Proc. Am. Math. Soc. 53 (1975), 435-439. (1975) Zbl0276.52006MR0383254DOI10.1090/S0002-9939-1975-0383254-5
  21. Lutwak, E., 10.1007/BF02759811, Isr. J. Math. 28 (1977), 249-253. (1977) Zbl0363.52009MR0464070DOI10.1007/BF02759811
  22. Lutwak, E., Yang, D., Zhang, G., 10.1016/j.aim.2009.08.002, Adv. Math. 223 (2010), 220-242. (2010) Zbl05643962MR2563216DOI10.1016/j.aim.2009.08.002
  23. Lv, S., 10.1007/s10711-009-9414-x, Geom. Dedicata 145 (2010), 169-180. (2010) Zbl1202.52008MR2600953DOI10.1007/s10711-009-9414-x
  24. Schneider, R., 10.1017/CBO9781139003858, Encyclopedia of Mathematics and its Applications 151, Cambridge University Press, Cambridge (2014). (2014) Zbl1287.52001MR3155183DOI10.1017/CBO9781139003858
  25. Schuster, F. E., 10.1112/S0025579300000103, Mathematica 53 (2006), 211-234. (2006) Zbl1129.52002MR2343256DOI10.1112/S0025579300000103
  26. Schuster, F. E., 10.1016/j.aim.2008.05.001, Adv. Math. 219 (2008), 344-368. (2008) Zbl1146.52003MR2435426DOI10.1016/j.aim.2008.05.001
  27. Schuster, F. E., 10.1215/00127094-2010-033, Duke Math. J. 154 (2010), 1-30. (2010) Zbl1205.52004MR2668553DOI10.1215/00127094-2010-033
  28. Schuster, F. E., Wannerer, T., 10.1353/ajm.2015.0041, Am. J. Math. 137 (2015), 1651-1683. (2015) Zbl1336.52020MR3432270DOI10.1353/ajm.2015.0041
  29. Schuster, F. E., Wannerer, T., 10.4171/JEMS/801, J. Eur. Math. Soc. (JEMS) 20 (2018), 1851-1884. (2018) Zbl1398.52018MR3854893DOI10.4171/JEMS/801
  30. Zhang, T., Wang, W., 10.1007/s11859-016-1157-6, Wuhan Univ. J. Nat. Sci. 21 (2016), 185-190. (2016) Zbl1363.26055MR3525752DOI10.1007/s11859-016-1157-6
  31. Zhao, C.-J., 10.1007/s10711-010-9487-6, Geom. Dedicata 149 (2010), 373-378. (2010) Zbl1207.52009MR2737698DOI10.1007/s10711-010-9487-6
  32. Zhao, C.-J., 10.7146/math.scand.a-15220, Math. Scand. 111 (2012), 147-160. (2012) Zbl1281.52006MR3001365DOI10.7146/math.scand.a-15220
  33. Zhao, C.-J., 10.1007/s12044-015-0227-6, Proc. Indian Acad. Sci., Math. Sci. 125 (2015), 209-219. (2015) Zbl1321.52014MR3361514DOI10.1007/s12044-015-0227-6
  34. Zhao, C.-J., 10.1007/s12220-015-9598-2, J. Geom. Anal. 26 (2016), 1523-1538. (2016) Zbl1350.52004MR3472843DOI10.1007/s12220-015-9598-2
  35. Zhao, C.-J., Cheung, W.-S., 10.1007/s10711-010-9568-6, Geom. Dedicata 154 (2011), 81-91. (2011) Zbl1230.52023MR2832712DOI10.1007/s10711-010-9568-6
  36. Zhao, C.-J., Mihály, B., Width-integrals of mixed projection bodies and mixed affine surface area, Gen. Math. 19 (2011), 123-133. (2011) Zbl1224.52016MR2788350
  37. Zhou, Y., 10.22436/jnsa.010.08.30, J. Nonlinear Sci. Appl. 10 (2017), 4372-4380. (2017) Zbl1412.52005MR3702585DOI10.22436/jnsa.010.08.30

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