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

Karp, L.; Peyerimhoff, N.

Authors

L. Karp



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.

Citation

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

Journal Article Type Article
Publication Date 2002
Journal Archiv der Mathematik
Print ISSN 0003-889X
Electronic ISSN 1420-8938
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 79
Pages 223-231
DOI https://doi.org/10.1007/s00013-002-8308-z