迈斯纳多面体的密度

IF 0.5 4区数学 Q3 MATHEMATICS

Geometriae Dedicata Pub Date : 2024-07-19 DOI:10.1007/s10711-024-00933-z

Ryan Hynd

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引用次数: 0

摘要

我们考虑的是\(\mathbb {R}^3\) 中的迈斯纳多面体。这些多面体是恒宽体，其边界由球体碎片和锭环组成。我们通过取全等球的适当交点来定义这些形状，并证明它们在豪斯多夫拓扑的恒宽体空间中是致密的。这一密度论断基本上是由萨利建立的。不过，考虑到最近在理解球多面体和基于这些形状构建恒宽体方面取得的进展，我们提出了一个现代观点。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

The density of Meissner polyhedra

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The density of Meissner polyhedra

We consider Meissner polyhedra in \(\mathbb {R}^3\). These are constant width bodies whose boundaries consist of pieces of spheres and spindle tori. We define these shapes by taking appropriate intersections of congruent balls and show that they are dense within the space of constant width bodies in the Hausdorff topology. This density assertion was essentially established by Sallee. However, we offer a modern viewpoint taking into consideration the recent progress in understanding ball polyhedra and in constructing constant width bodies based on these shapes.

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来源期刊

Geometriae Dedicata 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Geometriae Dedicata concentrates on geometry and its relationship to topology, group theory and the theory of dynamical systems. Geometriae Dedicata aims to be a vehicle for excellent publications in geometry and related areas. Features of the journal will include: A fast turn-around time for articles. Special issues centered on specific topics. All submitted papers should include some explanation of the context of the main results. Geometriae Dedicata was founded in 1972 on the initiative of Hans Freudenthal in Utrecht, the Netherlands, who viewed geometry as a method rather than as a field. The present Board of Editors tries to continue in this spirit. The steady growth of the journal since its foundation is witness to the validity of the founder''s vision and to the success of the Editors'' mission.