GENERAL $L_p$-INTERSECTION BODIES

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

“…In the meantime, they ( [26,27]) also showed that if τ = 0, then I 0 p K = I p K and 9) for all u ∈ S n−1 . From (1.4), (1.5) and (1.7), we easily obtain for τ ∈ [−1, 1] (see [27]),…”

“…Recently, Wang and Li ([26,27]) introduced the notion of general L p -intersection body with a parameter τ as follows: For K ∈ S n o , 0 < p < 1 and 5) for all u ∈ S n−1 , where…”

“…For the general L p -intersection bodies, Wang and Li in [27] obtained the following extremum values of volume and a Brunn-Minkowski type inequality with respect to L q (q > 0) radial combinations of star bodies, respectively.…”

Inequalities on asymmetric Lp-harmonic radial bodies

“…The asymmetric L p -Brunn-Minkowski theory is far more general since the continuous parameter makes the L p -asymmetric geometric bodies can be studied by analytical methods. In the past ten years, the investigations of L p -asymmetric geometric bodies have received great interest from many articles (see [2,10,16,17,19,20,22,[24][25][26][27][28][29]). …”

Busemann-Petty Problems for Quasi Lp Intersection Bodies

“…The intersection bodies have been intensively studied in recent years (see [20][21][22][23][24][25][26][27][28] and the books [19,29]). From (3) and the fact that star bodies and satisfy ⊆ if and only if ( , ⋅) ≤ ( , ⋅), we see that the Busemann-Petty problem can be rephrased in the following way: for , ∈ S , is it true that ⊆ ⇒ [30][31][32][33][34][35][36][37][38][39][40][41]).…”