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

Karp, L.; Peyerimhoff, N.

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
• Public URL: https://durham-repository.worktribe.com/output/1586385