, Volume 79, Issue 3, pp 223-231

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

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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.