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Images of reduction operators. (English) Zbl 0458.30026


MSC:

30F20 Classification theory of Riemann surfaces
31A20 Boundary behavior (theorems of Fatou type, etc.) of harmonic functions in two dimensions
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References:

[1] Constantinescu, C., & A. Cornea, Ideale Ränder Riemannscher Flächen. Berlin Heidelberg New York: Springer 1963.
[2] Glasner, M., & R. Katz, On the behavior of solutions of {\(\Delta\)}u=Pu at the Royden boundary. J. d’Analyse Math. 22, 345–354 (1969). · Zbl 0179.15201
[3] Glasner, M., & M. Nakai, Riemannian manifolds with discontinuous metrics and the Dirichlet integral. Nagoya Math. J. 46, 1–48 (1972). · Zbl 0212.45002
[4] Glasner, M., & M. Nakai, The roles of nondensity points. Duke Math. J. 43, 579–595 (1976). · Zbl 0341.31001
[5] Nakai, M., · Zbl 0226.31006
[6] Nakai, M., Order comparisons on canonical isomorphisms. Nagoya Math. J. 50, 67–87 (1973) · Zbl 0271.31002
[7] Nakai, M., Canonical isomorphisms of energy finite solutions of {\(\Delta\)}u=Pu on open Riemann surfaces. Nagoya Math. J. 56, 79–84 (1974). · Zbl 0304.31003
[8] Nakai, M., Extremizations and Dirichlet integrals on Riemann surfaces. J. Math. Soc. Japan 28, 581–603 (1976). · Zbl 0323.30021
[9] Nakai, M., An example on canonical isomorphism. Nagoya Math. J. 70, 25–40 (1978). · Zbl 0408.31003
[10] Royden, H., The equation {\(\Delta\)}u=Pu, and the classification of open Riemann surfaces. Ann. Acad. Sci. Fenn. 271, 27 pp. (1959). · Zbl 0096.05803
[11] Sario, L., & M. Nakai, Classification theory of Riemann surfaces. Berlin Heidelberg New York: Springer 1970. · Zbl 0199.40603
[12] Singer, I., Dirichlet finite solutions of {\(\Delta\)}u=Pu. Proc. Amer. Math. Soc. 32, 464–468 (1972). · Zbl 0243.31002
[13] Singer, I., Boundary isomorphisms between Dirichlet finite solutions of {\(\Delta\)}u= Pu and harmonic functions. Nagoya Math. J. 50, 7–20 (1973). · Zbl 0272.31001
[14] Sternberg, S., Lectures on differential geometry. Englewood Cliffs, N.J.: PrenticeHall 1964. · Zbl 0129.13102
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