Dirichlet finite solutions of Δ𝑢=𝑃𝑢, and classification of Riemann surfaces

DOI10.1090/S0002-9904-1971-12705-2zbMath0223.30010OpenAlexW1500916656MaRDI QIDQ5628426

Mitsuru Nakai

Publication date: 1971

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

Full work available at URL: https://doi.org/10.1090/s0002-9904-1971-12705-2

Mathematics Subject Classification ID

Compact Riemann surfaces and uniformization (30F10) Harmonic functions on Riemann surfaces (30F15) Classification theory of Riemann surfaces (30F20)

Related Items (12)

Riemannian Manifolds with Discontinuous Metrics and the Dirichlet Integral ⋮ A remark on classification of Riemannian manifolds with respect to Δ𝑢=𝑃𝑢 ⋮ Relations between boundaries of a riemannian manifold ⋮ Positiveness of the Reproducing Kernel in the Space PD(R) ⋮ Dirichlet finite solutions of $\Delta u=Pu$ on open Riemann surfaces ⋮ A remark on classification of Riemann surfaces with respect to Δ𝑢=𝑃𝑢 ⋮ Riemannian Manifolds with Discontinuous Metrics and the Dirichlet Integral ⋮ Banach spaces of bounded solutions of Δu = Pu (P ≥ 0) on hyperbolic riemann surfaces ⋮ Integration near the Royden boundary of a Riemannian manifold ⋮ Integration near the Royden boundary of a Riemannian manifold ⋮ The equation \(\Delta u=Pu\) on \(E^m\) with almost rotation free \(P\geq O\). ⋮ The equation \(\Delta u=Pu\) on the unit disk with almost rotation free \(P\geq 0\).

Cites Work

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• On the behavior of solutions of \(\Delta u = Pu\) at the Royden boundary
• The Space of Dirichlet-Finite Solutions of the Equation Δu = Pu on a Riemann Surface
• Classification of Riemann surfaces
• Harmonic Functions on Open Riemann Surfaces

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