q-dual mixed volumes and L p -intersection bodies

In this paper, we introduce the new notions of {L_{p}} -intersection and mixed intersection bodies. Inequalities for the q-dual volume sum of {L_{p}} -mixed intersection bodies are established.

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

For 0 < p < 1, the notions of symmetric and asymmetric Lp-intersection bodies were introduced by Haberl and Ludwig. Recently, Wang and Li defined the general Lp-intersection bodies. In this paper, associated with the Lp-dual affine surface areas, we give the extremum values of the general Lp-intersection bodies. Moreover, a Brunn-Minkowski type inequality and a monotone inequality for the Lp-dual affine surface area version of general Lp-intersection bodies are established, respectively.

Busemann-Petty Problems for Quasi Lp Intersection Bodies

We investigate the Lp dual geominimal surface area and volume forms of Busemann-Petty problems for the quasi Lp intersection bodies and establish some new geometric inequalities. Our results provide a significant complement to the researches on Busemann-Petty problems for intersection bodies.