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Archiv der Mathematik

, Volume 79, Issue 3, pp 223–231 | Cite as

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

  • L. Karp
  • N. Peyerimhoff
Article

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.

Keywords

Fixed Base Hyperbolic Plane Geometric Description Unique Minimum Regular Polygon 

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Copyright information

© Birkhäuser Verlag, Basel 2002

Authors and Affiliations

  • L. Karp
    • 1
  • N. Peyerimhoff
    • 2
  1. 1.Department of Mathematics, CUNY Graduate Center and Lehman College, 365 Fifth Avenue, New York, NY 10016, USA,¶ e-mail: lkarp@gc.cuny.eduUSA
  2. 2.Fakultät für Mathematik, Ruhr-Universität Bochum, Universitätsstr. 150, Gebäude NA 5/32, D-44780 Bochum, Germany,¶ e-mail: peyerim@math.ruhr-uni-bochum.deGermany

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