相关论文: The Dual Orlicz-Brunn-Minkowski Theory
This paper develops basic setting for the dual Orlicz-Brunn-Minkowski theory for star bodies. An Orlicz $\varphi$-radial addition of two or more star bodies is proposed and related dual Orlicz-Brunn-Minkowski inequality is established.…
Recently, Gardner, Hug and Weil have introduced the Orlicz-Brunn-Minkowski theory: a general framework, additions, and inequalities. Following this, in the paper we consider Orlicz dual Brunn-Minkowski theory. We introduce Orlicz hormonic…
The Orlicz-Brunn-Minkowski theory, introduced by Lutwak, Yang, and Zhang, is a new extension of the classical Brunn-Minkowski theory. It represents a generalization of the $L_p$-Brunn-Minkowski theory, analogous to the way that Orlicz…
The general volume of a star body, a notion that includes the usual volume, the $q$th dual volumes, and many previous types of dual mixed volumes, is introduced. A corresponding new general dual Orlicz curvature measure is defined that…
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…
Analogues of the classical inequalities from the Brunn-Minkowski theory for rotation intertwining additive maps of convex bodies are developed. Analogues are also proved of inequalities from the dual Brunn-Minkowski theory for intertwining…
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 paper, we consider the concept of $C$-star body in a fixed pointed closed convex cone $C$ and study the dual mixed volume for $C$-star bodies. For $C$-star bodies, we establish the corresponding dual Brunn-Minkowski inequality, the…
This paper aims to develop basic theory for the dual Orlicz $L_{\phi}$ affine and geominimal surface areas for star bodies, which belong to the recent dual Orlicz-Brunn-Minkowski theory for star bodies. Basic properties for these new affine…
This paper gives a systematic study to the general dual-polar Orlicz-Minkowski problem (e.g., Problem \ref{general-dual-polar}). This problem involves the general dual volume $\widetilde{V}_G(\cdot)$ recently proposed in \cite{GHWXY, GHXY}…
In this paper, the Orlicz addition of measures is proposed and an interpretation of the $f$-divergence is provided based on a linear Orlicz addition of two measures. Fundamental inequalities, such as, a dual functional…
In the paper, our main aim is to generalize the width integrals to the Orlicz space. Under the framework of Orlicz Brunn-Minkowski theory, we introduce a new affine geometric quantity by calculating Orlicz first order variation of the width…
B\"or\"oczky, Lutwak, Yang and Zhang recently proved the log-Brunn-Minkowski inequality which is stronger than the classical Brunn-Minkowski inequality for two origin-symmetric convex bodies in the plane. This paper establishes the…
Lutwak's notion of affine quermassintegrals of a convex body quickly became of great importance in convex and affine geometry and more recently, also in asymptotic geometric analysis. In this note we introduce the notion of Orlicz mixed…
In this paper, the dual Orlicz curvature measure is proposed and its basic properties are provided. A variational formula for the dual Orlicz-quermassintegral is established in order to give a geometric interpretation of the dual Orlicz…
Let $C$ be a closed convex cone in ${\mathbb R}^n$, pointed and with interior points. We consider sets of the form $A=C\setminus A^\bullet$, where $A^\bullet\subset C$ is a closed convex set. If $A$ has finite volume (Lebesgue measure),…
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…
\footnotesize B\"{o}r\"{o}czky, Lutwak, Yang and Zhang recently conjectured a certain strengthening of the Brunn-Minkowski inequality for symmetric convex bodies, the so-called log-Brunn-Minkowski inequality. We establish this inequality…
In this paper, we first introduce a new concept of {\it dual quermassintegral sum function} of two star bodies and establish Minkowski's type inequality for dual quermassintegral sum of mixed intersection bodies, which is a general form of…
This paper establishes two new geometric inequalities in the dual Brunn-Minkowski theory. The first, originally conjectured by Lutwak, is the Brunn-Minkowski inequality for dual quermassintegrals of origin-symmetric convex bodies. The…