Geodesic
Lp-DUAL MIXED GEOMINIMAL SURFACE AREA
Glasgow mathematical journal, Tome 56 (2014) no. 1, pp. 229-239

Voir la notice de l'article provenant de la source Cambridge University Press

Lutwak (Adv. Math., vol. 118(2), 1996, pp. 244–294) defined the notion of Lp-geominimal surface area based on Lp-mixed volumes. Recently, Wang and Qi (J. Inequal. Appl., vol. 2011, 2011, pp. 1–10) introduced the concept of Lp-dual geominimal surface area based on Lp-dual mixed volumes. In this paper, based on Lp-dual mixed quermassintegrals, we define the concept of Lp-dual mixed geominimal surface area and establish several inequalities for this new notion.
DOI : 10.1017/S0017089513000244
Mots-clés : 52A20, 52A40 
FENG, YIBIN; WANG, WEIDONG. Lp-DUAL MIXED GEOMINIMAL SURFACE AREA. Glasgow mathematical journal, Tome 56 (2014) no. 1, pp. 229-239. doi: 10.1017/S0017089513000244
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     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089513000244/}
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[1] 1.Alesker, S., Bernig, A. and Schuster, F. E., Harmonic analysis of translation invariant valuations, Geom. Funct. Anal. 21 (2011), 751–773. Google Scholar

[2] 2.Gardner, R. J., Geometric tomography, 2nd edn. (Cambridge University Press, Cambridge, UK, 2006). Google Scholar

[3] 3.Gardner, R. J., Koldobsky, A. and Schlumprecht, T., An analytic solution to the Busemann-Petty problem on sections of convex bodies, Ann. Math. 149 (1999), 691–703. Google Scholar

[4] 4.Haberl, C., L -intersection bodies, Adv. Math. 217 (6) (2008), 2599–2624. Google Scholar | DOI

[5] 5.Hardy, G. H., Littlewood, J. E. and Pólya, G., Inequalities (Cambridge University Press, Cambridge, UK, 1959). Google Scholar

[6] 6.Ludwig, M., Intersection bodies and valuations, Amer. J. Math. 128 (2006), 1409–1428. Google Scholar | DOI

[7] 7.Ludwig, M., General affine surface areas, Adv. Math. 224 (2010), 2346–2360. Google Scholar

[8] 8.Ludwig, M. and Reitzner, M., A characterization of affine surface area, Adv. Math. 147 (1999), 138–172. Google Scholar

[9] 9.Ludwig, M. and Reitzner, M., A classification of SL(n) invariant valuations, Ann. Math. 172 (2010), 1223–1271. Google Scholar

[10] 10.Lutwak, E., Dual mixed volumes, Pacific J. Math. 58 (1975), 531–538. Google Scholar | DOI

[11] 11.Lutwak, E., Volume of mixed bodies, Trans. Amer. Math. Soc. 294 (2) (1986), 487–500. Google Scholar | DOI

[12] 12.Lutwak, E., Mixed affine surface area, J. Math. Anal. Appl. 125 (1987), 351–360. Google Scholar | DOI

[13] 13.Lutwak, E., Intersection bodies and dual mixed volumes, Adv. Math. 71 (1988), 232–261. Google Scholar

[14] 14.Lutwak, E., Centroid bodies and dual mixed volumes, Proc. Lond. Math. Soc. 60 (1990), 365–391. Google Scholar | DOI

[15] 15.Lutwak, E., The Brunn–Minkowski–Firey theory II: Affine and geominimal surface areas, Adv. Math. 118 (2) (1996), 244–294. Google Scholar | DOI

[16] 16.Parapatits, L. and Schuster, F. E., The Steiner formula for Minkowski valuations, Adv. Math. 230 (2012), 978–994. Google Scholar

[17] 17.Petty, C. M., Geominimal surface area, Geom. Dedicata 3 (1) (1974), 77–97. Google Scholar | DOI

[18] 18.Schneider, R., Convex bodies: the Brunn–Minkowski theory (Cambridge University Press, Cambridge, UK, 1993). Google Scholar

[19] 19.Schuster, F. E., Volume inequalities and additive maps of convex bodies, Mathematika 53 (2006), 211–234. Google Scholar

[20] 20.Schuster, F. E., Crofton measures and Minkowski valuations, Duke Math. J. 154 (2010), 1–30. Google Scholar

[21] 21.Stancu, A. and Werner, E., New higher-order equiaffine invariants, Israel J. Math. 171 (2009), 221–235. Google Scholar

[22] 22.Wang, W. D. and Feng, Y. B., A general L -version of Petty's affine projection inequality, Taiwan J. Math. 17 (2) (2013), 517–528. Google Scholar | DOI

[23] 23.Wang, W. D. and Leng, G. S., L -dual mixed quermassintegrals, Indian J. Pure Appl. Math. 36 (4) (2005), 177–188. Google Scholar

[24] 24.Wang, W. D. and Qi, C., L -dual geominimal surface area, J. Inequal. Appl. 2011 (2011), 1–10. Google Scholar

[25] 25.Werner, E., On L -affine surface areas, Indiana Univ. Math. J. 56 (2007), 2305–2323. Google Scholar

[26] 26.Werner, E. and Ye, D., New L -affine isoperimetric inequalities, Adv. Math. 218 (2008), 762–780. Google Scholar

[27] 27.Zhang, G. Y., A positive solution to the Busemann–Petty problem in ℝ4, Ann. Math. 149 (1999), 535–543. Google Scholar

[28] 28.Zhu, B. C., Li, N. and Zhou, J. Z., Isoperimetric inequalities for L -geominimal surface area, Glasg. Math. J. 53 (2011), 717–726. Google Scholar

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