伪锥体

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics Pub Date : 2024-01-04 DOI:10.1016/j.aam.2023.102657

Rolf Schneider

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引用次数: 0

摘要

伪凸是一类不包含原点的无界封闭凸集。它们具有一种极性，称为共极性。因此，它们可以被视为内部包含原点的凸体的对应物。下文的目的是更详细地研究这种类比。我们将对共极性的研究进行补充，例如考虑共轭面。然后，我们处理闵科夫斯基定理提出的问题，即哪些度量是给定衰退锥的伪锥的表面积度量。我们为可能的无限度量和一类特殊的伪圆锥提供了充分条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Pseudo-cones

Pseudo-cones are a class of unbounded closed convex sets, not containing the origin. They admit a kind of polarity, called copolarity. With this, they can be considered as a counterpart to convex bodies containing the origin in the interior. The purpose of the following is to study this analogy in greater detail. We supplement the investigation of copolarity, considering, for example, conjugate faces. Then we deal with the question suggested by Minkowski's theorem, asking which measures are surface area measures of pseudo-cones with given recession cone. We provide a sufficient condition for possibly infinite measures and a special class of pseudo-cones.

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来源期刊

Advances in Applied Mathematics 数学-应用数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

85 days

期刊介绍： Interdisciplinary in its coverage, Advances in Applied Mathematics is dedicated to the publication of original and survey articles on rigorous methods and results in applied mathematics. The journal features articles on discrete mathematics, discrete probability theory, theoretical statistics, mathematical biology and bioinformatics, applied commutative algebra and algebraic geometry, convexity theory, experimental mathematics, theoretical computer science, and other areas. Emphasizing papers that represent a substantial mathematical advance in their field, the journal is an excellent source of current information for mathematicians, computer scientists, applied mathematicians, physicists, statisticians, and biologists. Over the past ten years, Advances in Applied Mathematics has published research papers written by many of the foremost mathematicians of our time.