Title:
|
Inequalities for general width-integrals of Blaschke-Minkowski homomorphisms (English) |
Author:
|
Li, Chao |
Author:
|
Wang, Weidong |
Language:
|
English |
Journal:
|
Czechoslovak Mathematical Journal |
ISSN:
|
0011-4642 (print) |
ISSN:
|
1572-9141 (online) |
Volume:
|
70 |
Issue:
|
3 |
Year:
|
2020 |
Pages:
|
767-779 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
We establish some inequalities for general width-integrals of Blaschke-Minkowski homomorphisms. As applications, inequalities for width-integrals of projection bodies are derived. (English) |
Keyword:
|
general width-integral |
Keyword:
|
volume difference type inequality |
Keyword:
|
Blaschke-Minkowski homomorphism |
Keyword:
|
Brunn-Minkowski type inequality |
Keyword:
|
projection body |
MSC:
|
52A20 |
MSC:
|
52A40 |
idZBL:
|
07250688 |
idMR:
|
MR4151704 |
DOI:
|
10.21136/CMJ.2020.0521-18 |
. |
Date available:
|
2020-09-07T09:38:28Z |
Last updated:
|
2022-10-03 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148327 |
. |
Reference:
|
[1] Beckenbach, E., Bellman, R.: Inequalities.Ergebnisse der Mathematik und Ihrer Grenzgebiete 30, Springer, New York (1965). Zbl 0126.28002, MR 0192009, 10.1007/978-3-642-64971-4 |
Reference:
|
[2] Berg, A., Parapatits, L., Schuster, F. E., Weberndorfer, M.: Log-concavity properties of Minkowski valuations.Trans. Am. Math. Soc. 370 (2018), 5245-5277. Zbl 1390.52024, MR 3787383, 10.1090/tran/7434 |
Reference:
|
[3] Blaschke, W.: Vorlesungen über Integralgeometrie.German VEB Deutscher Verlag der Wissenschaften, Berlin (1955). Zbl 0066.40703, MR 0076373 |
Reference:
|
[4] Cheung, W.-S., Zhao, C.-J.: Width-integrals and affine surface area of convex bodies.Banach J. Math. Anal. 2 (2008), 70-77. Zbl 1155.52005, MR 2404711, 10.15352/bjma/1240336275 |
Reference:
|
[5] Dresher, M.: Moment spaces and inequalities.Duke Math. J. 20 (1953), 261-271. Zbl 0050.28202, MR 0055389, 10.1215/s0012-7094-53-02026-2 |
Reference:
|
[6] Feng, Y.: General mixed width-integral of convex bodies.J. Nonlinear Sci. Appl. 9 (2016), 4226-4234. Zbl 1347.52004, MR 3530126, 10.22436/jnsa.009.06.64 |
Reference:
|
[7] Feng, Y., Wang, W.: Blaschke-Minkowski homomorphisms and affine surface area.Publ. Math. 85 (2014), 297-308. Zbl 1340.52006, MR 3291832, 10.5486/PMD.2014.5903 |
Reference:
|
[8] Feng, Y., Wang, W., Yuan, J.: Inequalities of quermassintegrals about mixed Blaschke Minkowski homomorphisms.Tamkang J. Math. 46 (2015), 217-227. Zbl 1338.52005, MR 3406352, 10.5556/j.tkjm.46.2015.1689 |
Reference:
|
[9] Feng, Y., Wu, S.: Brunn-Minkowski type inequalies for width-integrals of index $i$.J. Comput. Anal. Appl. 24 (2018), 1408-1418. MR 3753402 |
Reference:
|
[10] Feng, Y., Wu, S., Wang, W.: Mixed chord-integrals of index $i$ and radial Blaschke-Minkowski homomorphisms.Rocky Mt. J. Math. 47 (2017), 2627-2640. Zbl 1385.52005, MR 3760310, 10.1216/RMJ-2017-47-8-2627 |
Reference:
|
[11] Firey, W. J.: Mean cross-section measures of harmonic means of convex bodies.Pac. J. Math. 11 (1961), 1263-1266. Zbl 0122.41101, MR 0140003, 10.2140/pjm.1961.11.1263 |
Reference:
|
[12] Gardner, R. J.: Geometric Tomography.Encyclopedia of Mathematics and Its Applications 58, Cambridge University Press, Cambridge (2006). Zbl 1102.52002, MR 2251886, 10.1017/CBO9781107341029 |
Reference:
|
[13] Haberl, C.: Minkowski valuations intertwining with the special linear group.J. Eur. Math. Soc. (JEMS) 14 (2012), 1565-1597. Zbl 1270.52018, MR 2966660, 10.4171/JEMS/341 |
Reference:
|
[14] Cifre, M. A. Hernández, Nicolás, J. Yepes: On Brunn-Minkowski-type inequalities for polar bodies.J. Geom. Anal. 26 (2016), 143-155. Zbl 1339.52007, MR 3441506, 10.1007/s12220-014-9541-y |
Reference:
|
[15] Ji, L., Zeng, Z.: Some inequalities for radial Blaschke-Minkowski homomorphisms.Czech. Math. J. 67 (2017), 779-793. Zbl 06770130, MR 3697916, 10.21136/CMJ.2017.0180-16 |
Reference:
|
[16] Li, Y., Wang, W.: Monotonicity inequalities for $L_p$ Blaschke-Minkowski homomorphism.J. Inequal. Appl. 2014 (2014), Article ID 131, 10 pages. Zbl 1310.52003, MR 3253878, 10.1186/1029-242X-2014-131 |
Reference:
|
[17] Li, X.-Y., Zhao, C.-J.: On the $p$-mixed affine surface area.Math. Inequal. Appl. 17 (2014), 443-450. Zbl 1296.52004, MR 3235022, 10.7153/mia-17-33 |
Reference:
|
[18] Lu, F., Leng, G.: On inequalities for $i$th width-integrals of convex bodies.Math. Appl. 19 (2006), 632-636 Chinese. Zbl 1101.52001, MR 2254976 |
Reference:
|
[19] Ludwig, M.: Minkowski valuations.Trans. Am. Math. Soc. 357 (2005), 4191-4213. Zbl 1077.52005, MR 2159706, 10.1090/S0002-9947-04-03666-9 |
Reference:
|
[20] Lutwak, E.: Width-integrals of convex bodies.Proc. Am. Math. Soc. 53 (1975), 435-439. Zbl 0276.52006, MR 0383254, 10.1090/S0002-9939-1975-0383254-5 |
Reference:
|
[21] Lutwak, E.: Mixed width-integrals of convex bodies.Isr. J. Math. 28 (1977), 249-253. Zbl 0363.52009, MR 0464070, 10.1007/BF02759811 |
Reference:
|
[22] Lutwak, E., Yang, D., Zhang, G.: Orlicz projection bodies.Adv. Math. 223 (2010), 220-242. Zbl 05643962, MR 2563216, 10.1016/j.aim.2009.08.002 |
Reference:
|
[23] Lv, S.: Dual Brunn-Minkowski inequality for volume differences.Geom. Dedicata 145 (2010), 169-180. Zbl 1202.52008, MR 2600953, 10.1007/s10711-009-9414-x |
Reference:
|
[24] Schneider, R.: Convex Bodies: The Brunn-Minkowski Theory.Encyclopedia of Mathematics and its Applications 151, Cambridge University Press, Cambridge (2014). Zbl 1287.52001, MR 3155183, 10.1017/CBO9781139003858 |
Reference:
|
[25] Schuster, F. E.: Volume inequalities and additive maps of convex bodies.Mathematica 53 (2006), 211-234. Zbl 1129.52002, MR 2343256, 10.1112/S0025579300000103 |
Reference:
|
[26] Schuster, F. E.: Valuations and Busemann-Petty type problems.Adv. Math. 219 (2008), 344-368. Zbl 1146.52003, MR 2435426, 10.1016/j.aim.2008.05.001 |
Reference:
|
[27] Schuster, F. E.: Crofton measures and Minkowski valuations.Duke Math. J. 154 (2010), 1-30. Zbl 1205.52004, MR 2668553, 10.1215/00127094-2010-033 |
Reference:
|
[28] Schuster, F. E., Wannerer, T.: Even Minkowski valuations.Am. J. Math. 137 (2015), 1651-1683. Zbl 1336.52020, MR 3432270, 10.1353/ajm.2015.0041 |
Reference:
|
[29] Schuster, F. E., Wannerer, T.: Minkowski valuations and generalized valuations.J. Eur. Math. Soc. (JEMS) 20 (2018), 1851-1884. Zbl 1398.52018, MR 3854893, 10.4171/JEMS/801 |
Reference:
|
[30] Zhang, T., Wang, W.: Inequalities for mixed width-integrals.Wuhan Univ. J. Nat. Sci. 21 (2016), 185-190. Zbl 1363.26055, MR 3525752, 10.1007/s11859-016-1157-6 |
Reference:
|
[31] Zhao, C.-J.: On Blaschke-Minkowski homomorphisms.Geom. Dedicata 149 (2010), 373-378. Zbl 1207.52009, MR 2737698, 10.1007/s10711-010-9487-6 |
Reference:
|
[32] Zhao, C.-J.: On polars of Blaschke-Minkowski homomorphisms.Math. Scand. 111 (2012), 147-160. Zbl 1281.52006, MR 3001365, 10.7146/math.scand.a-15220 |
Reference:
|
[33] Zhao, C.-J.: Volume sums of polar Blaschke-Minkowski homomorphisms.Proc. Indian Acad. Sci., Math. Sci. 125 (2015), 209-219. Zbl 1321.52014, MR 3361514, 10.1007/s12044-015-0227-6 |
Reference:
|
[34] Zhao, C.-J.: On Blaschke-Minkowski homomorphisms and radial Blaschke-Minkowski homomorphisms.J. Geom. Anal. 26 (2016), 1523-1538. Zbl 1350.52004, MR 3472843, 10.1007/s12220-015-9598-2 |
Reference:
|
[35] Zhao, C.-J., Cheung, W.-S.: Radial Blaschke-Minkowski homomorphisms and volume differences.Geom. Dedicata 154 (2011), 81-91. Zbl 1230.52023, MR 2832712, 10.1007/s10711-010-9568-6 |
Reference:
|
[36] Zhao, C.-J., Mihály, B.: Width-integrals of mixed projection bodies and mixed affine surface area.Gen. Math. 19 (2011), 123-133. Zbl 1224.52016, MR 2788350 |
Reference:
|
[37] Zhou, Y.: General $L_p$-mixed width-integral of convex bodies and related inequalities.J. Nonlinear Sci. Appl. 10 (2017), 4372-4380. Zbl 1412.52005, MR 3702585, 10.22436/jnsa.010.08.30 |
. |