多边形的模空间和有边界多面体的变形

IF 0.5 4区数学 Q3 MATHEMATICS Geometriae Dedicata Pub Date : 2023-12-13 DOI:10.1007/s10711-023-00834-7

Sasha Anan’in, Dmitrii Korshunov

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引用次数: 0

摘要

我们证明了伊恩-阿戈尔（Ian Agol）的一个猜想：有边界的多面体表面的所有等距变现都会在与边界同构的多边形的卡波维奇-米尔森模空间中扫出一个各向同性子集。对于一般的多面体圆盘，我们证明其等距实现的边界构成了一个拉格朗日子集。作为这一结果的应用，我们得出结论：一般等边多边形不可能是穹顶的（在肯扬、格拉兹林和帕克问题的意义上）。

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Moduli spaces of polygons and deformations of polyhedra with boundary

We prove a conjecture of Ian Agol: all isometric realizations of a polyhedral surface with boundary sweep out an isotropic subset in the Kapovich-Millson moduli space of polygons isomorphic to the boundary. For a generic polyhedral disk we show that boundaries of its isometric realizations make up a Lagrangian subset. As an application of this result, we conclude that a generic equilateral polygon cannot be domed (in the sense of a problem of Kenyon, Glazyrin and Pak).

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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.

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