Lp-dual three mixed quermassintegrals

Zhao, Chang-Jian; Bencze, Mihály

doi:10.2478/auom-2021-0030

Abstract

In the paper, the concept of L_p-dual three-mixed quermassintegrals is introduced. The formula for the L_p-dual three-mixed quermassintegrals with respect to the p-radial addition is proved. Inequalities of L_p-Minkowski, and Brunn-Minkowski type for the L_p-dual three-mixed quermassintegrals are established. The new L_p-Minkowski inequality is obtained that generalize a family of Minkowski type inequalities. The L_p-Brunn-Minkowski inequality is used to obtain a series of Brunn-Minkowski type inequalities.

References

[1] Y. D. Burago, V. A. Zalgaller, Geometric Inequalities, Springer-Verlag, Berlin-New york, 1988.10.1007/978-3-662-07441-1
Search in Google Scholar Back to article
[2] R. J. Gardner, Geometric Tomography, Cambridge Univ. Press, New York, 1996.
Search in Google Scholar Back to article
[3] R. J. Gardner, The Brunn-Minkowski inequality, Bull. Amer. Math. Soc., 39 (2002), 355–405.10.1090/S0273-0979-02-00941-2
Search in Google Scholar Back to article
[4] E. Grinberg, G. Zhang, Convolutions, transforms, and convex bodies, Proc. London Math. Soc,. 78 (1999), 77-115.10.1112/S0024611599001653
Search in Google Scholar Back to article
[5] E. Lutwak, Intersection bodies and dual mixed volumes, Adv. Math., 71 (1988), 232–261.10.1016/0001-8708(88)90077-1
Search in Google Scholar Back to article
[6] E. Lutwak, Dual mixed volumes, Pacific J. Math., 58 (1975), 531–538.10.2140/pjm.1975.58.531
Search in Google Scholar Back to article
[7] R. Schneider, Convex Bodies: The Brunn-Minkowski Theory, Cambridge Univ. Press, Second Edition, 2014.10.1017/CBO9781139003858
Search in Google Scholar Back to article
[8] W. Wang, G. Leng, Lp-dual mixed quermassintegrals, Indian J. Pure Appl. Math., 36 (2005), 177–188.
Search in Google Scholar Back to article
[9] D. Ye, Dual Orlicz-Brunn-Minkowski theory: dual Orlicz Lϕ affine and geominimal surface areas, J. Math. Anal. Appl., 443 (2016), 352–371.10.1016/j.jmaa.2016.05.027
Search in Google Scholar Back to article
[10] C.-J. Zhao, The dual logarithmic Aleksandrov-Fenchel inequality, Balkan J. Geom. Appl., 25 (2020), 157–169.
Search in Google Scholar Back to article
[11] C.-J. Zhao, Orlicz dual mixed volumes, Results Math., 68 (2015), 93–104.10.1007/s00025-014-0424-0
Search in Google Scholar Back to article
[12] C.-J. Zhao, Orlicz dual affine quermassintegrals, Forum Mathematicum, 30 (4) (2018), 929–945.10.1515/forum-2017-0174
Search in Google Scholar Back to article

Lp-dual three mixed quermassintegrals

Abstract

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