𝑃𝐷-minimal solutions of Δ𝑢=𝑃𝑢 on open Riemann surfaces

Ow, Wellington H.

doi:10.1090/S0002-9939-1973-0310233-4

$PD$-minimal solutions of $\Delta u=Pu$ on open Riemann surfaces
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by Wellington H. Ow

Proc. Amer. Math. Soc. 37 (1973), 85-91

DOI: https://doi.org/10.1090/S0002-9939-1973-0310233-4

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Abstract:

By means of the Royden compactification of an open Riemann surface R necessary and sufficient conditions are given for a Dirichlet-finite solution of $\Delta u = Pu\;(P \geqq 0, P\;{\nequiv }\;0)$ to be PD-minimal on R. A relation between PD-minimal solutions and HD-minimal solutions is obtained. In addition it is shown that the dimension of the space of PD-solutions is the same as the number of P-energy nondensity points in the finite dimensional case.

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