[1] Abardia, J., Bernig, A.: Projection bodies in complex vector spaces. Adv. Math. 227 (2011), 830-846. DOI 10.1016/j.aim.2011.02.013 | MR 2793024 | Zbl 1217.52009

[2] Alesker, S., Bernig, A., Schuster, F. E.: Harmonic analysis of translation invariant valuations. Geom. Funct. Anal. 21 (2011), 751-773. DOI 10.1007/s00039-011-0125-8 | MR 2827009 | Zbl 1228.53088

[3] Beckenbach, E. F., Bellman, R.: Inequalities. Ergebnisse der Mathematik und ihrer Grenzgebiete. Neue Folge, Band 30, Springer, Berlin (1965). MR 0192009 | Zbl 0126.28002

[4] Gardner, R. J.: A positive answer to the Busemann-Petty problem in three dimensions. Ann. Math. (2) 140 (1994), 435-447. DOI 10.2307/2118606 | MR 1298719 | Zbl 0826.52010

[5] Gardner, R. J.: Intersection bodies and the Busemann-Petty problem. Trans. Am. Math. Soc. 342 (1994), 435-445. DOI 10.2307/2154703 | MR 1201126 | Zbl 0801.52005

[6] Gardner, R. J.: The Brunn-Minkowski inequality. Bull. Am. Math. Soc., New Ser. 39 (2002), 355-405. DOI 10.1090/S0273-0979-02-00941-2 | MR 1898210 | Zbl 1019.26008

[7] Gardner, R. J., Hug, D., Weil, W.: The Orlicz-Brunn-Minkowski theory: a general framework, additions, and inequalities. J. Differ. Geom. 97 (2014), 427-476. DOI 10.4310/jdg/1406033976 | MR 3263511 | Zbl 1303.52002

[8] Gardner, R. J., Hug, D., Weil, W., Ye, D.: The dual Orlicz-Brunn-Minkowski theory. J. Math. Anal. Appl. 430 (2015), 810-829. DOI 10.1016/j.jmaa.2015.05.016 | MR 3351982 | Zbl 1320.52008

[9] Gardner, R. J., Koldobsky, A., Schlumprecht, T.: An analytic solution to the Busemann-Petty problem on sections of convex bodies. Ann. Math. (2) 149 (1999), 691-703. DOI 10.2307/120978 | MR 1689343 | Zbl 0937.52003

[10] Gardner, R. J., Parapatits, L., Schuster, F. E.: A characterization of Blaschke addition. Adv. Math. 254 (2014), 396-418. DOI 10.1016/j.aim.2013.11.017 | MR 3161103 | Zbl 1291.52011

[11] Haberl, C.: Star body valued valuations. Indiana Univ. Math. J. 58 (2009), 2253-2276. DOI 10.1512/iumj.2009.58.3685 | MR 2583498 | Zbl 1183.52003

[12] Koldobsky, A.: Intersection bodies, positive definite distributions, and the Busemann-Petty problem. Am. J. Math. 120 (1998), 827-840. DOI 10.1353/ajm.1998.0030 | MR 1637955 | Zbl 0914.52001

[13] Koldobsky, A.: Stability in the Busemann-Petty and Shephard problems. Adv. Math. 228 (2011), 2145-2161. DOI 10.1016/j.aim.2011.06.031 | MR 2836117 | Zbl 1228.52006

[14] Koldobsky, A., Ma, D.: Stability and slicing inequalities for intersection bodies. Geom. Dedicata 162 (2013), 325-335. DOI 10.1007/s10711-012-9729-x | MR 3009547 | Zbl 1261.52003

[15] Leng, G.: The Brunn-Minkowski inequality for volume differences. Adv. Appl. Math. 32 (2004), 615-624. DOI 10.1016/S0196-8858(03)00095-2 | MR 2042686 | Zbl 1056.52003

[16] Ludwig, M.: Projection bodies and valuations. Adv. Math. 172 (2002), 158-168. DOI 10.1016/S0001-8708(02)00021-X | MR 1942402 | Zbl 1019.52003

[17] Ludwig, M.: Intersection bodies and valuations. Am. J. Math. 128 (2006), 1409-1428. DOI 10.1353/ajm.2006.0046 | MR 2275906 | Zbl 1115.52007

[18] Lutwak, E.: Dual mixed volumes. Pac. J. Math. 58 (1975), 531-538. DOI 10.2140/pjm.1975.58.531 | MR 0380631 | Zbl 0273.52007

[19] Lutwak, E.: Intersection bodies and dual mixed volumes. Adv. Math. 71 (1988), 232-261. DOI 10.1016/0001-8708(88)90077-1 | MR 0963487 | Zbl 0657.52002

[20] Lutwak, E.: Inequalities for mixed projection bodies. Trans. Am. Math. Soc. 339 (1993), 901-916. DOI 10.2307/2154305 | MR 1124171 | Zbl 0784.52009

[21] Lutwak, E.: The Brunn-Minkowski-Firey theory I. Mixed volumes and the Minkowski problem. J. Differ. Geom. 38 (1993), 131-150. DOI 10.4310/jdg/1214454097 | MR 1231704 | Zbl 0788.52007

[22] Lutwak, E., Yang, D., Zhang, G.: Orlicz centroid bodies. J. Differ. Geom. 84 (2010), 365-387. DOI 10.4310/jdg/1274707317 | MR 2652465 | Zbl 1206.49050

[23] Lutwak, E., Yang, D., Zhang, G.: Orlicz projection bodies. Adv. Math. 223 (2010), 220-242. DOI 10.1016/j.aim.2009.08.002 | MR 2563216 | Zbl 05643962

[24] Schneider, R.: Convex Bodies: The Brunn-Minkowski Theory. Encyclopedia of Mathematics and Its Applications 151, Cambridge University Press, Cambridge (2014). DOI 10.1017/CBO9781139003858 | MR 3155183 | Zbl 1287.52001

[25] Schuster, F. E.: Volume inequalities and additive maps of convex bodies. Mathematika 53 (2006), 211-234. DOI 10.1112/S0025579300000103 | MR 2343256 | Zbl 1129.52002

[26] Schuster, F. E.: Valuations and Busemann-Petty type problems. Adv. Math. 219 (2008), 344-368. DOI 10.1016/j.aim.2008.05.001 | MR 2435426 | Zbl 1146.52003

[27] Wang, W.: $L_p$ Brunn-Minkowski type inequalities for Blaschke-Minkowski homomorphisms. Geom. Dedicata 164 (2013), 273-285. DOI 10.1007/s10711-012-9772-7 | MR 3054628 | Zbl 1280.52007

[28] Xi, D., Jin, H., Leng, G.: The Orlicz Brunn-Minkowski inequality. Adv. Math. 260 (2014), 350-374. DOI 10.1016/j.aim.2014.02.036 | MR 3209355 | Zbl 06298949

[29] Xiong, G., Zou, D.: Orlicz mixed quermassintegrals. Sci. China, Math. 57 (2014), 2549-2562. DOI 10.1007/s11425-014-4812-4 | MR 3275405 | Zbl 1328.52003

[30] Zhao, C.-J.: On radial Blaschke-Minkowski homomorphisms. Geom. Dedicata 167 (2013), 1-10. DOI 10.1007/s10711-012-9798-x | MR 3128767 | Zbl 1287.52009

[31] Zhao, C.-J.: Orlicz dual mixed volumes. Result. Math. 68 (2015), 93-104. DOI 10.1007/s00025-014-0424-0 | MR 3391494 | Zbl 1329.52008

[32] Zhao, C., Cheung, W.-S.: Radial Blaschke-Minkowski homomorphisms and volume differences. Geom. Dedicata 154 (2011), 81-91. DOI 10.1007/s10711-010-9568-6 | MR 2832712 | Zbl 1230.52023

[33] Zhao, C.-J., Leng, G.: Brunn-Minkowski inequality for mixed intersection bodies. J. Math. Anal. Appl. 301 (2005), 115-123. DOI 10.1016/j.jmaa.2004.07.013 | MR 2105924 | Zbl 1065.52006

[34] Zhu, B., Zhou, J., Xu, W.: Dual Orlicz-Brunn-Minkowski theory. Adv. Math. 264 (2014), 700-725. DOI 10.1016/j.aim.2014.07.019 | MR 3250296 | Zbl 1307.52004