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Bounded Energy-Finite Solutions of Δu = Pu on a Riemannian Manifold

Published online by Cambridge University Press:  22 January 2016

Y.K. Kwon ,
L. Sario  and
J. Schiff
Y.K. Kwon
Affiliation:
University of California, Los Angeles
L. Sario
Affiliation:
University of California, Los Angeles
J. Schiff
Affiliation:
University of California, Los Angeles
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1. The classification of Riemann surfaces with respect to the equation Δu = Pu (P ≥ 0, P ≢ 0) was initiated by Ozawa [13] and further developed by L. Myrberg [8, 9], Royden [14], Nakai [10, 11], Sario-Nakai [15], Nakai-Sario [12], Glasner-Katz [3], and Kwon-Sario [7].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 42 , March 1971 , pp. 95 - 108
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1971

References

[1] Sario, J. Chang-L., Royden’s algebra on Riemannian spaces, Math. Scand. 27 (1970).Google Scholar
[2] Cornea, C. Constantinescu-A., Ideale Ränder RiemannscherFlächen, Springer, 1963, 244 pp.Google Scholar
[3] Katz, M. Glasner-R., On the behavior of solutions of Δu = Pu at the Royden boundary, J. Analyse Math. 22 (1969), 343–354.Google Scholar
[4] Stromberg, E. Hewitt-K., Real and abstract analysis, Springer, 1965, 476 pp.Google Scholar
[5] Sario, Y.K. Kwon-L., A maximum principle for bounded harmonic functions on Riemannian spaces, Canad. J. Math. 22 (1970), 847–854.Google Scholar
[6] Sario, Y.K. Kwon-L., Harmonic functions on a subregion of a Riemannian manifold, J. Ind. Math. Soc. (to appear).Google Scholar
[7] Sario, Y.K. Kwon-L., The P-singular point of the P-compactification for Δu — Pu , Bull. Amer. Math. Soc. (to appear).Google Scholar
[8] Myrberg, L., Über die Integration der Differentialgleichung Δu = c(P)u auf offenen Riemannschen Flächen, Math. Scand. 2 (1954), 142–152.Google Scholar
[9] Myrberg, L., Über die Existenz der Greenschen Funktion der Gleichung Δu = c(P)u auf Riemann schen Flächen, Ann. Acad. Sci. Fenn. Ser. A.I. 170 (1954), 8 pp.Google Scholar
[10] Nakai, M., The space of non-negative solutions of the equation Δu = pu on a Riemann surface, Ködai Math. Sem. Rep. 12 (1960), 151–178.Google Scholar
[11] Nakai, M., The space of Dirichlet-finite solutions of the equation Δu = Pu on a Riemann surface, Nagoya Math. J. 18 (1961), 111–131.CrossRefGoogle Scholar
[12] Sario, M. Nakai-L., A new operator for elliptic equations and the P-compatification for Δu = Pu , Math. Ann. 189 (1970), 242–256.Google Scholar
[13] Ozawa, M., A set of capacity zero and the equation Δu = Pu , Ködai Math. Sem. Rep. 12 (1960), 76–81.Google Scholar
[14] Royden, H.L., The equation Δu = Pu and the classification of open Riemann surfaces, Ann. Acad. Sci. Fenn. Ser. A.I. 271 (1959), 27 pp.Google Scholar
[15] Nakai, L. Sario-M., Classification theory of Riemann surfaces, Springer, 1970, 446 pp.Google Scholar