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On the Spectral Theory of the Laplacian on Compact Polyhedral Surfaces of Arbitrary Genus

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Computational Approach to Riemann Surfaces

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2013))

Abstract

There are several well-known ways to introduce a compact Riemann surface which are also discussed in the present volume, e.g., via algebraic equations or by means of some uniformization theorem, where the surface is introduced as the quotient of the upper half-plane over the action of a Fuchsian group. In this chapter we consider a less popular approach which is at the same time, perhaps, the most elementary: one can simply consider the boundary of a connecter (but, generally, not simply connected) polyhedron in three dimensional Euclidean space.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Blvd. West, Montreal, Quebec, H3G 1M8, Canada

    Alexey Kokotov

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  1. Alexey Kokotov
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Correspondence to Alexey Kokotov .

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Editors and Affiliations

  1. Institute of Mathematics, Technical University of Berlin, Straße des 17.Juni 136, Berlin, 10623, Germany

    Alexander I. Bobenko

  2. Institut de Mathématiques, Université de Bourgogne, av. Alain Savary 9, Dijon Cedex, 21078, France

    Christian Klein

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Kokotov, A. (2011). On the Spectral Theory of the Laplacian on Compact Polyhedral Surfaces of Arbitrary Genus. In: Bobenko, A., Klein, C. (eds) Computational Approach to Riemann Surfaces. Lecture Notes in Mathematics(), vol 2013. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17413-1_8

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