Geometry and Spectra of Compact Riemann Surfaces
Geometry and Spectra of Compact Riemann Surfaces
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DOI：
10.1007/978-0-8176-4992-0
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发表时间：
1992
期刊：
影响因子：
--
通讯作者：
P. Buser
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文献类型：
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作者：
P. Buser
本书涉及两个主题。第一科目是大于1的紧黎曼曲面的几何理论，第二科目是拉普拉斯算子及其与紧黎曼曲面几何的关系。这本书源于很久以前出版一篇 Habili-tionsschrift 论文的想法，在论文中我研究了 Bers 的裤子分解定理及其在紧致黎曼曲面谱中的应用。论文中的一个基本工具是与双曲测地多边形三角测量相关的剪切和粘贴。由于这种紧黎曼曲面的几何方法并没有以书籍的形式存在，因此我以这本书为契机详细地进行了几何研究，因此它增加了几章。另外，当我写东西的时候，这个领域取得了很大的进展，而且一些新的结果太具有挑战性，不能被排除在本书之外。例如，Sunada 构建的等谱流形非常令人着迷，我很长一段时间都沉迷于构建示例。随着时间的流逝，这本书不断增长。幸运的是，人们对存在性证明的兴趣也在不断增长。例如，编辑很感兴趣，我的家人也很感兴趣。于是这本书最终就形成了现在的形式。这里给出的许多证明都是新的，也有一些结果是首次在印刷品中出现。
This book deals with two subjects. The first subject is the geometric theory of compact Riemann surfaces of genus greater than one, the second subject is the Laplace operator and its relationship with the geometry of compact Riemann surfaces. The book grew out of the idea, a long time ago, to publish a Habili-tionsschrift, a thesis, in which I studied Bers' pants decomposition theorem and its applications to the spectrum of a compact Riemann surface. A basic tool in the thesis was cutting and pasting in connection with the trigono metry of hyperbolic geodesic polygons. As this approach to the geometry of a compact Riemann surface did not exist in book form, I took this book as an occasion to carry out the geometry in detail, and so it grew by several chapters. Also, while I was writing things up there was much progress in the field, and some of the new results were too challenging to be left out of the book. For instance, Sunada's construction of isospectral manifolds was fascinating, and I got hooked on constructing examples for quite a while. So time went on and the book kept growing. Fortunately, the interest in exis tence proofs also kept growing. The editor, for instance, was interested, and so was my family. And so the book finally assumed its present form. Many of the proofs given here are new, and there are also results which appear for the first time in print.