紧凑黎曼曲面的直径

IF 0.6 4区 数学 Q3 MATHEMATICS Computational Methods and Function Theory Pub Date : 2024-06-27 DOI:10.1007/s40315-024-00546-3
Huck Stepanyants, Alan Beardon, Jeremy Paton, Dmitri Krioukov
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引用次数: 0

摘要

直径是几何物体最基本的属性之一,而黎曼曲面则是最基本的几何物体之一。令人惊讶的是,只有球面和环面的紧凑黎曼曲面的直径是精确已知的。对于更高的属面,只有非常宽泛但松散的上下限。由于高属面上一对点之间的距离没有简单的表达式,因此精确计算直径的问题一直难以解决。在这里,我们证明了一类被称为广义波尔萨曲面的简单黎曼曲面的直径等于其基本多边形的半径,且任何属都大于 1。这是第一个关于紧凑双曲流形直径的精确结果。
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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Diameter of Compact Riemann Surfaces

Diameter is one of the most basic properties of a geometric object, while Riemann surfaces are one of the most basic geometric objects. Surprisingly, the diameter of compact Riemann surfaces is known exactly only for the sphere and the torus. For higher genuses, only very general but loose upper and lower bounds are available. The problem of calculating the diameter exactly has been intractable since there is no simple expression for the distance between a pair of points on a high-genus surface. Here we prove that the diameters of a class of simple Riemann surfaces known as generalized Bolza surfaces of any genus greater than 1 are equal to the radii of their fundamental polygons. This is the first exact result for the diameter of a compact hyperbolic manifold.

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来源期刊
Computational Methods and Function Theory
Computational Methods and Function Theory MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
3.20
自引率
0.00%
发文量
44
审稿时长
>12 weeks
期刊介绍: CMFT is an international mathematics journal which publishes carefully selected original research papers in complex analysis (in a broad sense), and on applications or computational methods related to complex analysis. Survey articles of high standard and current interest can be considered for publication as well.
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