The classical Minkowski formula is extended to spacelike codimension-two submanifolds in spacetimes which admit “hidden symmetry” from conformal KillingYano two-forms. As an application, we obtain an Alexandrov type theorem for spacelike codimension-two submanifolds in a static spherically symmetric spacetime: a codimensiontwo submanifold with constant normalized null expansion (null mean curva...

It is well-known that the Hölder-Rogers inequality implies the Minkowski inequality. Infantozzi [6] observed implicitely and Royden [15] proved explicitely that the reverse implication is also true. In this note we discuss and give a new proof of this perhaps surprising fact. Mathematics subject classification (2000): 26D15.

Elaborating on the similarity between the entropy power inequality and the Brunn-Minkowski inequality, Costa and Cover conjectured in On the similarity of the entropy power inequality and the BrunnMinkowski inequality (IEEE Trans. Inform. Theory 30 (1984), no. 6, 837-839) the 1 n -concavity of the outer parallel volume of measurable sets as an analogue of the concavity of entropy power. We inve...

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

Abstract We investigate the weighted $L_p$ affine surface areas which appear in recently established Steiner formula of Brunn–Minkowski theory. show that they are valuations on set convex bodies and prove isoperimetric inequalities for them. related to f divergences cone measures body its polar, namely Kullback–Leibler divergence Rényi divergence.

Let ?n be the standard Gaussian measure on Rn. We prove that for every symmetric convex sets K,L in Rn and ??(0,1),?n(?K+(1??)L)1n???n(K)1n+(1??)?n(L)1n, thus settling a problem raised by Gardner Zvavitch (2010). This is analogue of classical Brunn–Minkowski inequality Lebesgue measure. also show that, fixed ??(0,1), equality attained if only K=L.