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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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