Keywords: characterization; radial Minkowski additive operator; radial Minkowski homomorphism
@article{10_21136_CMJ_2021_0366_19,
author = {Ji, Lewen},
title = {Radial {Minkowski} additive operators},
journal = {Czechoslovak Mathematical Journal},
pages = {641--654},
year = {2021},
volume = {71},
number = {3},
doi = {10.21136/CMJ.2021.0366-19},
mrnumber = {4295236},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2021.0366-19/}
}
Ji, Lewen. Radial Minkowski additive operators. Czechoslovak Mathematical Journal, Tome 71 (2021) no. 3, pp. 641-654. doi: 10.21136/CMJ.2021.0366-19
[1] Abardia-Evéquoz, J., Colesanti, A., Gómez, E. Saorín: Minkowski additive operators under volume constraints. J. Geom. Anal. 28 (2018), 2422-2455. | DOI | MR | JFM
[2] Abardia-Evéquoz, J., Colesanti, A., Gómez, E. Saorín: Minkowski valuations under volume constraints. Adv. Math. 333 (2018), 118-158. | DOI | MR | JFM
[3] Alesker, S.: Continuous rotation invariant valuations on convex sets. Ann. Math. (2) 149 (1999), 977-1005. | DOI | MR | JFM
[4] Chen, B., Rota, G.-C.: Totally invariant set functions of polynomial type. Commun. Pure Appl. Math. 47 (1994), 187-197. | DOI | MR | JFM
[5] Colesanti, A., Ludwig, M., Mussnig, F.: Minkowski valuations on convex functions. Calc. Var. Partial Differ. Equ. 56 (2017), Article ID 162, 29 pages. | DOI | MR | JFM
[6] Dorrek, F.: Minkowski endomorphisms. Geom. Funct. Anal. 27 (2017), 466-488. | DOI | MR | JFM
[7] Dulio, P., Gardner, R. J., Peri, C.: Characterizing the dual mixed volume via additive functionals. Indiana Univ. Math. J. 65 (2016), 69-91. | DOI | MR | JFM
[8] Gardner, R. J.: A positive answer to the Busemann-Petty problem in three dimensions. Ann. Math. (2) 140 (1994), 435-447. | DOI | MR | JFM
[9] Gardner, R. J.: Intersection bodies and the Busemann-Petty problem. Trans. Am. Math. Soc. 342 (1994), 435-445. | DOI | MR | JFM
[10] Gardner, R. J., Koldobski, A., Schlumprecht, T.: An analytical solution to the Busemann-Petty problem on sections of convex bodies. Ann. Math. (2) 149 (1999), 691-703. | DOI | MR | JFM
[11] Grinberg, E., Zhang, G.: Convolutions, transforms, and convex bodies. Proc. Lond. Math. Soc., III. Ser. 78 (1999), 77-115. | DOI | MR | JFM
[12] Guo, L., Jia, H.: The dual Blaschke addition. J. Geom. Anal. 30 (2020), 3026-3034. | DOI | MR | JFM
[13] Ji, L., Zeng, Z.: Some inequalities for radial Blaschke-Minkowski homomorphisms. Czech. Math. J. 67 (2017), 779-793. | DOI | MR | JFM
[14] Kiderlen, M.: Blaschke- and Minkowski-endomorphisms of convex bodies. Trans. Am. Math. Soc. 358 (2006), 5539-5564. | DOI | MR | JFM
[15] Klain, D. A.: Star valuations and dual mixed volumes. Adv. Math. 121 (1996), 80-101. | DOI | MR | JFM
[16] Klain, D. A.: Invariant valuations on star-shaped sets. Adv. Math. 125 (1997), 95-113. | DOI | MR | JFM
[17] Ludwig, M.: Intersection bodies and valuations. Am. J. Math. 128 (2006), 1409-1428. | DOI | MR | JFM
[18] Lutwak, E.: Dual mixed volumes. Pac. J. Math. 58 (1975), 531-538. | DOI | MR | JFM
[19] Lutwak, E.: Intersection bodies and dual mixed volumes. Adv. Math. 71 (1988), 232-261. | DOI | MR | JFM
[20] Schneider, R.: On Steiner point of convex bodies. Isr. J. Math. 9 (1971), 241-249. | DOI | MR | JFM
[21] Schneider, R.: Equivariant endomorphisms of the space of convex bodies. Trans. Am. Math. Soc. 194 (1974), 53-78. | DOI | MR | JFM
[22] Schneider, R.: Convex Bodies: The Brunn-Minkowski Theory. Encyclopedia of Mathematics and its Applications 151. Cambridge University Press, Cambridge (2014). | DOI | MR | JFM
[23] Schuster, F. E.: Volume inequalities and additive maps of convex bodies. Mathematika 53 (2006), 211-234. | DOI | MR | JFM
[24] Schuster, F. E.: Convolutions and multiplier transformations of convex bodies. Trans. Am. Math. Soc. 359 (2007), 5567-5591. | DOI | MR | JFM
[25] Schuster, F. E.: Valuations and Busemann-Petty type problems. Adv. Math. 219 (2008), 344-368. | DOI | MR | JFM
[26] Tradacete, P., Villanueva, I.: Radial continuous valuations on star bodies. J. Math. Anal. Appl. 454 (2017), 995-1018. | DOI | MR | JFM
[27] Tradacete, P., Villanueva, I.: Continuity and representation of valuations on star bodies. Adv. Math. 329 (2018), 361-391. | DOI | MR | JFM
[28] Villanueva, I.: Radial continuous rotation invariant valuations on star bodies. Adv. Math. 291 (2016), 961-981. | DOI | MR | JFM
[29] Wang, W., Liu, L.: Fourier transform and valuations. J. Math. Anal. Appl. 470 (2019), 1167-1184. | DOI | MR | JFM
[30] Zhang, G.: A positive solution to the Busemann-Petty problem in $\mathbb R^4$. Ann. Math. (2) 149 (1999), 535-543. | DOI | MR | JFM
[31] Zhao, C.-J.: On Blaschke-Minkowski homomorphisms and radial Blaschke-Minkowski homomorphisms. J. Geom. Anal. 26 (2016), 1523-1538. | DOI | MR | JFM
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