三角多边形和半三角多边形的填充密度

IF 0.9 3区物理与天体物理 Q2 MATHEMATICS

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2023-10-29 DOI:10.3842/sigma.2023.081

Du, Yu, Kosmacher, Gabriel, Liu, Yichen, Massman, Jeff, Palmer, Joseph, Thieme, Timothy, Wu, Jerry, Zhang, Zheyu

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引用次数: 0

摘要

利用具有Delzant多边形和半半多边形的四维环可积系统和半可积系统之间的关系，我们开发了计算这些系统的某些等变填充密度和等变容量的技术。这扩展了Pelayo和Pelayo- schmidt的结果。我们计算了几个重要例子的密度，并利用我们的技术解决了等变半完整填充问题，即，我们列出了所有的半多边形，其相关的半系统允许一个等变填充，该填充填充了流形的一组测度零之外的所有半多边形。本文也作为一个简明易懂的介绍，Delzant多边形和半多边形在四维。

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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Packing Densities of Delzant and Semitoric Polygons

Exploiting the relationship between 4-dimensional toric and semitoric integrable systems with Delzant and semitoric polygons, respectively, we develop techniques to compute certain equivariant packing densities and equivariant capacities of these systems by working exclusively with the polygons. This expands on results of Pelayo and Pelayo-Schmidt. We compute the densities of several important examples and we also use our techniques to solve the equivariant semitoric perfect packing problem, i.e., we list all semitoric polygons for which the associated semitoric system admits an equivariant packing which fills all but a set of measure zero of the manifold. This paper also serves as a concise and accessible introduction to Delzant and semitoric polygons in dimension four.

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来源期刊

Symmetry Integrability and Geometry-Methods and Applications 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Scope Geometrical methods in mathematical physics Lie theory and differential equations Classical and quantum integrable systems Algebraic methods in dynamical systems and chaos Exactly and quasi-exactly solvable models Lie groups and algebras, representation theory Orthogonal polynomials and special functions Integrable probability and stochastic processes Quantum algebras, quantum groups and their representations Symplectic, Poisson and noncommutative geometry Algebraic geometry and its applications Quantum field theories and string/gauge theories Statistical physics and condensed matter physics Quantum gravity and cosmology.