[1] Barthe F. The Brunn-Minkowski theorem and related geometric and functional inequalities. Proceedings of the International Congress of Mathematicians, Madrid, Spain, 2006
[2] Gardner R J. The Brunn-Minkowski inequality. Bull Amer Math Soc, 2002, 39:355-405
[3] Gardner R J. Geometric Tomography. Second ed. Encyclopedia Math Appl. Vol 58. New York:Cambridge University Press, 2006
[4] Gardner R J. The dual Brunn-Minkowski theory for bounded Borel sets:Dual affine quermassintegrals and inequalities. Adv Math, 2007, 216:358-386
[5] Gardner R J, Hug D, Weil W. Operations between sets in geometry. Eur Math Soc, 2013, 15:2297-2352
[6] Gardner R J, Hug D, Weil W. The Orlicz-Brunn-Minkowski theory:a general framework, additions, and inequalities. Differential Geom, 2014, 97:427-476
[7] Gardner R J, Hug D, Weil W, Ye D. The Dual Orlicz-Brunn-Minkowski Theory. Math Anal Appl, 2015, 430:810-829
[8] Gruber P M. Convex and discrete geometry. Grundlehren der Mathematischen Wiseenschaften. Vol 336. Berlin:Springer, 2007
[9] Haberl C, Lutwak E, Yang D, Zhang G. The even Orlicz Minkowski problem. Adv Math, 2010, 224:2485-2510
[10] Hadwiger H. Vorlesungen Über Inhalt, Oberfläche und Isoperimetrie. Berlin:Springer-Verlag, 1957
[11] Huang H, Lutwak E, Yang D, Zhang G. Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems. Adv Math, 2016, 216:325-388
[12] Klain D A, Rota G-C. Introduction to geometric probability. Cambridge:Cambridge University Press, 1997
[13] Li D, Zou D, Xiong G. Orlicz mixed affine quermassintegrals. Sci China Math, 2015, 58:1715-1722
[14] Lutwak E. Dual mixed volumes. Pacific J Math, 1975, 58:531-538
[15] Lutwak E. Mean dual and harmonic cross-sectional measures. Ann Mat Pura Appl, 1979, 119:139-148
[16] Lutwak E. A general isepiphanic inequality. Proc Amer Soc, 1984, 90:415-421
[17] Lutwak E. Inequalities for Hadwiger's harmonic quermassintegrals. Math Ann, 1988, 280:165-175
[18] Lutwak E. Intersection bodies and dual mixed volumes. Adv Math, 1988, 71:232-261
[19] Lutwak E. The Brunn-Minkowski-Firey theory. I. Mixed volumes and the Minkowski problem. Differential Geom, 1993, 38:131-150
[20] Lutwak E, Yang D, Zhang G. Orlicz projection bodies. Adv Math, 2010, 223:220-242
[21] Lutwak E, Yang D, Zhang G. Orlicz centroid bodies. Differential Geom, 2010, 84:365-387
[22] Lutwak E, Yang D, Zhang G. The Brunn-Minkowski-Firey inequality for nonconvex sets. Adv Appl Math, 2012, 48:407-413
[23] Ren D L. Topics in Integral Geometry. Singapore:World Scientific, 1994
[24] Santaló L A. Integral Geometry and Geometric Probability. Cambridge:Cambridge University Press, 2004
[25] Schneider R. Convex bodies:the Brunn-Minkowski theory. Cambridge:Cambridge University Press, 2014
[26] Schneider R, Weil W. Stochastic and Integral Geometry. Berlin:Springer, 2008
[27] Thompson A C. Minkowski geometry. Encyclopedia Math Appl. Vol 63. Cambridge:Cambridge University Press, 1996
[28] Xi D, Jin H, Leng G. The Orlicz Brunn-Minkowski inequality. Adv Math, 2014, 260:350-374
[29] Xiong G, Zou D. Orlicz mixed quermassintegrals. Sci China Math, 2014, 57:2549-2562
[30] Ye D. Dual Orlicz-Brunn-Minkowski theory:dual Orlicz Lφ affine and geominimal surface areas. J Math Anal Appl, 2016, 443:352-371
[31] Yuan J, Yuan S, Leng G. Inequalities for dual harmonic quermassintegrals. J Korean Math Soc, 2006, 43:593-607
[32] Zhang G. Dual kinematic formulas. Trans Amer Math Soc, 1999, 351:985-995
[33] Zou D, Zhou J, Xu W. Dual Orlicz-Brunn-Minkowski theory. Adv Math, 2014, 264:700-725
[34] Zou D, Xiong G. Orlicz-John ellipsoids. Adv Math, 2014, 265:132-168
[35] Zou D, Xiong G. Orlicz-Legendre ellipsoids. J Geom Analy, 2016, 26:2474-2502
[36] Zou D, Xiong G. A unified treatment for Brunn-Minkowski type inequality. Commun Anal Geom, in press |