Every covering of a compact Riemann surface of genus greater than one carries a nontrivial \(L^ 2\) harmonic differential

DOI10.1007/BF02392190zbMath0541.30035OpenAlexW2066305850MaRDI QIDQ794806

Józef Dodziuk

Publication date: 1984

Published in: Acta Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02392190

zbMATH Keywords

capacityisoperimetric inequalityKleinian group\(L^ 2\) harmonic differentialcovering of a compact Riemann surface

Mathematics Subject Classification ID

Compact Riemann surfaces and uniformization (30F10) Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Partial differential equations on manifolds; differential operators (58J99) Capacity and harmonic measure in the complex plane (30C85) Differentials on Riemann surfaces (30F30)

Related Items (3)

On the hyperbolicity of certain planar domains ⋮ Difference Equations, Isoperimetric Inequality and Transience of Certain Random Walks ⋮ Analytic continuation of holonomy germs of Riccati foliations along Brownian paths

Cites Work

• On the theory of covering surfaces.
• Open Riemann surfaces and extremal problems on compact subregions
• Prolongements analytiques au sens de Riemann
• The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature
• Behavior of diffusion semi-groups at infinity
• L 2 -Cohomology of Noncompact Surfaces
• The Conformal Group of a Plane Domain
• On a Metric Property of Fuchsian Groups
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