CMC-1 surfaces via osculating Möbius transformations between circle patterns

IF 1.2 2区数学 Q1 MATHEMATICS

Transactions of the American Mathematical Society Pub Date : 2024-01-17 DOI:10.1090/tran/9121

Wai Yeung Lam

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引用次数: 0

Abstract

Given two circle patterns of the same combinatorics in the plane, the Möbius transformations mapping circumdisks of one to the other induce a P S L ( 2 , C ) PSL(2,\mathbb {C}) -valued function on the dual graph. Such a function plays the role of an osculating Möbius transformation and induces a realization of the dual graph in hyperbolic space. We characterize the realizations and obtain a one-to-one correspondence in the cases that the two circle patterns share the same discrete conformal structure. These correspondences are analogous to the Weierstrass representation for surfaces with constant mean curvature H ≡ 1 H\equiv 1 in hyperbolic space. We further establish convergence on triangular lattices.

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通过圆图案之间的莫比乌斯环形变换获得 CMC-1 曲面

给定平面上相同组合的两个圆图案，将其中一个的圆盘映射到另一个的莫比乌斯变换会在对偶图上诱导出一个 P S L ( 2 , C ) PSL(2,\mathbb {C}) 值函数。这样的函数扮演着循环莫比乌斯变换的角色，并诱导出对偶图在双曲空间中的实现。我们描述了这些实现，并在两个圆图具有相同离散共形结构的情况下获得了一一对应关系。这些对应关系类似于双曲空间中具有恒定平均曲率 H ≡ 1 H\equiv 1 的曲面的魏尔斯特拉斯表示。我们进一步建立了三角网格上的收敛性。

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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来源期刊

Transactions of the American Mathematical Society 数学-数学

CiteScore

2.30

自引率

7.70%

发文量

171

审稿时长

3-6 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles in all areas of pure and applied mathematics. To be published in the Transactions, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Papers of less than 15 printed pages that meet the above criteria should be submitted to the Proceedings of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.