Archiv der Mathematik

, Volume 79, Issue 3, pp 223–231

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

  • L. Karp
  • N. Peyerimhoff

DOI: 10.1007/s00013-002-8308-z

Cite this article as:
Karp, L. & Peyerimhoff, N. Arch. Math. (2002) 79: 223. doi:10.1007/s00013-002-8308-z


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.

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.eduUS
  2. 2.Fakultät für Mathematik, Ruhr-Universität Bochum, Universitätsstr. 150, Gebäude NA 5/32, D-44780 Bochum, Germany,¶ e-mail: