奥尔利茨调和版的双混合卷

IF 0.7 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications Pub Date : 2025-07-02 DOI:10.1016/j.difgeo.2025.102268

Chang-Jian Zhao

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引用次数: 0

摘要

本文的主要目的是将对偶混合调和quermass积分推广到Orlicz空间。在Orlicz对偶Brunn-Minkowski理论的框架下，通过计算对偶混合调和quermass积分的Orlicz一阶变分，引入了一个新的仿射几何量，称为Orlicz对偶混合调和quermass积分。将对偶混合调和quermass积分的基本概念和结论以及对偶调和quermass积分的Minkowski不等式和Brunn-Minkowski不等式推广到一个Orlicz集合中，并将Orlicz对偶混合体积的相关概念和不等式也包含在我们的结论中。

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Orlicz harmonic version of dual mixed volumes

In the paper, our main aim is to generalize the dual mixed harmonic quermassintegrals to Orlicz space. Under the framework of Orlicz dual Brunn-Minkowski theory, we introduce a new affine geometric quantity by calculating Orlicz first order variation of the dual mixed harmonic quermassintegrals, and call it the Orlicz dual mixed harmonic quermassintegrals. The fundamental notions and conclusions of the dual mixed harmonic quermassintegrals and the Minkowski and Brunn-Minkowski inequalities for the dual harmonic quermassintegrals are extended to an Orlicz setting, and the related concepts and inequalities of Orlicz dual mixed volumes are also included in our conclusions.

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来源期刊

Differential Geometry and its Applications 数学-数学

CiteScore

1.00

自引率

20.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.