论文信息 - Monotonicity inequalities for Lp Blaschke-Minkowski homomorphisms

Monotonicity inequalities for Lp Blaschke-Minkowski homomorphisms

Schuster introduced the notion of Blaschke-Minkowski homomorphism and considered its Shephard problems. Wang gave the definition of Lp Blaschke-Minkowski homomorphisms and considered its Shephard problems for volume. In this paper, we obtain its Shephard type inequalities for the affine surface area and two monotonicity inequalities for Lp Blaschke-Minkowski homomorphisms are established.MSC:52A20, 52A40.

Weidong Wang | Yanan Li | Weidong Wang | Yanan Li

[1] Gaoyong Zhang,et al. Convolutions, Transforms, and Convex Bodies , 1999 .

[2] Peter McMullen,et al. Valuations on convex bodies , 1983 .

[3] Daniel A. Klain,et al. Introduction to Geometric Probability , 1997 .

[4] E. Lutwak. Mixed affine surface area , 1987 .

[5] Franz E Schuster. Convolutions and multiplier transformations of convex bodies , 2007, 1207.7252.

[6] Lp Blaschke-Minkowski homomorphisms , 2013 .

[7] Franz E Schuster. Volume inequalities and additive maps of convex bodies , 2006, 1207.7290.

[8] Minkowski Valuations,et al. Minkowski Valuations , 2004 .

[9] Continuous rotation invariant valuations on convex sets , 1999, math/9905204.

[10] Weidong Wang,et al. L_p-mixed affine surface area , 2017 .

[11] R. Gardner. Geometric Tomography: Parallel X-rays of planar convex bodies , 2006 .

[12] H. Hadwiger. Vorlesungen über Inhalt, Oberfläche und Isoperimetrie , 1957 .

[13] S. Alesker. Description of translation invariant valuations on convex sets with solution of P. McMullen's conjecture , 2001 .

[14] Erwin Lutwak,et al. The Brunn–Minkowski–Firey Theory II: Affine and Geominimal Surface Areas , 1996 .

[15] K. Ball. CONVEX BODIES: THE BRUNN–MINKOWSKI THEORY , 1994 .

[16] M. Ludwig. Ellipsoids and matrix-valued valuations , 2003 .

[17] P. McMullen. Valuations and Dissections , 1993 .

[18] Wm. J. Firey,et al. $p$-Means of Convex Bodies. , 1962 .