Lp -dual geominimal surface areas for the general Lp-intersection bodies

Abstract

For 0 < p < 1, Haberl and Ludwig defined the notions of symmetric and asymmetric L p -intersection bodies. Recently, Wang and Li introduced the general L p -intersection bodies. In this paper, we give the L p -dual geominimal surface area forms for the extremum values and Brunn-Minkowski type inequality of general L p -intersection bodies. Further, combining with the L p -dual geominimal surface areas, we consider Busemann-Petty type problem for general L p -intersection bodies.

Dual mixed complex brightness integrals

“…Further, they [8] defined the asymmetric L p -intersection bodies. Based on this notion, Wang and Li [33,34] defined the general L p -intersection body, (also see [25,28]). The family of intersection bodies and mixed intersection bodies are valuable in geometry analysis, many important results were obtained (see [7,27]).…”

General Blaschke Bodies and the Asymmetric Negative Solutions of Shephard Problem

“…The right inequality of (9) is proved. From the equality condition of (27), the equality holds in (28) if and only if M and −M are homothetic if γ = ±1. That is to say, M is a centrally symmetric convex body.…”

Some inequalities for the (p,q)-mixed geominimal surface areas and Lp radial Blaschke-Minkowski homomorphisms

“…If L = K or q = n in (4), then from (2) or (3) we see that the definition is just Lutwak's L p geominimal surface area for p ≥ 1 (see [17]). For the studies of L p geominimal surface areas, some results have been obtained in these articles (see e.g., [2,4,12,21,22,25,[27][28][29][30][37][38][39]).…”