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Extremal properties of the principal Dirichlet eigenvalue for regular polygons in the hyperbolic plane

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Abstract.

We prove that amongst all hyperbolic triangles of equal perimeter or quadrilaterals in a given geodesic ball the regular polygon is the unique minimum for the first Dirichlet eigenvalue. Moreover, we give a geometric description of the set of all hyperbolic triangles with a fixed base and prescribed area.

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Authors and Affiliations

  1. Department of Mathematics, CUNY Graduate Center and Lehman College, 365 Fifth Avenue, New York, NY 10016, USA,¶ e-mail: lkarp@gc.cuny.edu, USA

    L. Karp

  2. Fakultät für Mathematik, Ruhr-Universität Bochum, Universitätsstr. 150, Gebäude NA 5/32, D-44780 Bochum, Germany,¶ e-mail: peyerim@math.ruhr-uni-bochum.de, Germany

    N. Peyerimhoff

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  1. L. Karp
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  2. N. Peyerimhoff
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Eingegangen am 23. 8. 2000

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Karp, L., Peyerimhoff, N. Extremal properties of the principal Dirichlet eigenvalue for regular polygons in the hyperbolic plane. Arch. Math. 79, 223–231 (2002). https://doi.org/10.1007/s00013-002-8308-z

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  • DOI: https://doi.org/10.1007/s00013-002-8308-z

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