The Poincaré metric and isoperimetric inequalities for hyperbolic polygons

DOI10.1090/S0002-9947-05-03946-2zbMath1075.30016OpenAlexW1877396081MaRDI QIDQ5461368

Petros Hadjicostas, Alexander Yu. Solynin, Roger W. Barnard

Publication date: 26 July 2005

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-05-03946-2

zbMATH Keywords

isoperimetric inequalitypolygonhyperbolic geometryconformal radiusEuler gamma functionPoincaré metricabsolutely monotonic function

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Extremal problems for conformal and quasiconformal mappings, other methods (30C75)

Related Items (5)

Condenser capacity and hyperbolic perimeter ⋮ Estimates on kernel functions of elliptically schlicht domains ⋮ Exercises on the theme of continuous symmetrization ⋮ Quadratic differentials and conformal invariants ⋮ Topics in special functions. II

Cites Work

• Solution of a Pólya-Szegö isoperimetric problem
• Some extremal problems for circular polygons
• An isoperimetric inequality for logarithmic capacity of polygons
• Euclidean and Non-Euclidean Geometries Without Continuity
• Hyperbolic geometry: The first 150 years
• Isoperimetric Inequalities on Surfaces of Constant Curvature
• Some extremal problems on the hyperbolic polygons
• On some inequalities for the gamma and psi functions
• Isoperimetric Inequalities in Mathematical Physics. (AM-27)
• Inequalities: theory of majorization and its applications
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