Related papers: The mixed affine quermassintegrals
We prove a version of the Aleksandrov-Fenchel inequality for mixed volumes of coconvex bodies. This version is motivated by an inequality from commutative algebra relating intersection multiplicities of ideals.
This paper continues the study of Alexandrov-Fenchel inequalities for quermassintegrals for $k$-convex domains. It focuses on the application to the Michael-Simon type inequalities for $k$-curvature operators. The proof uses optimal…
By calculating the first order variation of the dual mixed volumes, we put forward a new concept Orlicz multiple dual mixed volumes. The classical dual mixed volumes and dual Aleksandrov-Fenchel inequality are generalized to the Orlicz…
In this paper, the mixed Lp-surface area measures are defined and the mixed Lp Minkowski inequality is obtained consequently. Furthermore, the mixed Lp projection inequality for mixed projection bodies is established.
In this paper, we derive new sharp weighted Alexandrov-Fenchel and Minkowski inequalities for smooth, closed hypersurfaces under various convexity assumptions in Euclidean, spherical, and hyperbolic spaces. These inequalities extend…
In this paper, {we extend the affine dual curvature measures to the $L_p$ setting and solve the existence part of the corresponding Minkowski problem for non-symmetric discrete measures when $p>1$ and for symmetric measures when $p\geq0$.}…
We extend to a functional setting the concept of quermassintegrals, well-known within the Minkowski theory of convex bodies. We work in the class of quasi-concave functions defined on the Euclidean space, and with the hierarchy of their…
Various Alexandrov-Fenchel type inequalities have appeared and played important roles in convex geometry, matrix theory and complex algebraic geometry. It has been noticed for some time that they share some striking analogies and have…
In this paper, we find some new sharp bounds for $\left(\sin x\right) /x$, which unify and refine Jordan, Adamovi\'{c}-Mitrinovi\'{c}and and Cusa's inequalities. As applications of main results, some new Shafer-Fink type inequalities for…
Mixed $f$-divergences, a concept from information theory and statistics, measure the difference between multiple pairs of distributions. We introduce them for log concave functions and establish some of their properties. Among them are…
In this paper we define an addition operation on the class of quasi-concave functions. While the new operation is similar to the well-known sup-convolution, it has the property that it polarizes the Lebesgue integral. This allows us to…
In this paper we first establish an optimal Sobolev type inequality for hypersurfaces in $\H^n$(see Theorem \ref{mainthm1}). As an application we obtain hyperbolic Alexandrov-Fenchel inequalities for curvature integrals and…
In this paper, we first establish an equivalence theorem of Minkowski spaces by using results in centro-affine differential geometry. As an application in Finsler geometry, we gives some new characterizations of Berwald spaces.
Lutwak's volume inequalities for polar projection bodies of all orders are generalized to polarizations of Minkowski valuations generated by even, zonal measures on the Euclidean unit sphere. This is based on analogues of mixed projection…
In this paper, the concept of the classical $f$-divergence for a pair of measures is extended to the mixed $f$-divergence for multiple pairs of measures. The mixed $f$-divergence provides a way to measure the difference between multiple…
A generalization of the affine-geometric Wirtinger inequality for curves to hypersurfaces is given.
We introduce a affine geometric quantity and call it Orlicz mixed chord integral, which generalize the chord integrals to Orlicz space. Minkoswki and Brunn-Minkowski inequalities for the Orlicz mixed chord integrals are establish. These new…
In this paper, we establish an Orlicz log-Aleksandrov-Fenchel inequality by introducing new concepts of mixed volume measure and Orlicz multiple mixed volume measure, and using the Orlicz-Aleksandrov-Fenchel inequality. The Orlicz…
In this study, we obtain some new integral inequalities for different classes of convex functions by using some elementary inequalities and classical inequalities like general Cauchy inequality and Minkowski inequality.
In this paper, some new Gronwall type inequalities involving iterated integrals are given.