Glasner, Moses; Nakai, Mitsuru Order comparison of quasibounded solutions of d*du=uP on Riemann surfaces. (English) Zbl 0504.30036 Arch. Math. 39, 463-475 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 Review MSC: 30F20 Classification theory of Riemann surfaces 31A35 Connections of harmonic functions with differential equations in two dimensions 35J15 Second-order elliptic equations Keywords:hyperbolic Riemann surface; quasibounded solution; d*du=uP; ideal boundary PDFBibTeX XMLCite \textit{M. Glasner} and \textit{M. Nakai}, Arch. Math. 39, 463--475 (1982; Zbl 0504.30036) Full Text: DOI References: [1] M. Glasner andM. Nakai, Inextremization and boundedness on open Riemann surfaces. Math. Z.168, 1–13 (1979). · Zbl 0416.30040 [2] P. Loeb, An axiomatic treatment of pairs of elliptic differential equations. Ann. Inst. Fourier (Grenoble),16, 167–208 (1966). · Zbl 0172.15101 [3] P. Loeb andB. Walsh, A maximal regular boundary for solutions of elliptic differential equations. Ann. Inst. Fourier (Grenoble),18, 283–308 (1968). · Zbl 0167.40302 [4] L. Lumer-Naim,H p spaces of harmonic functions. Ann. Inst. Fourier (Grenoble),17, 425–469 (1967). · Zbl 0153.43102 [5] C.Miranda, Partial Differential Equations of Elliptic Type. Berlin-Heidelberg-New York 1970. · Zbl 0198.14101 [6] M. Nakai, The space of bounded solutions of the equation{\(\Delta\)}u=Pu on a Riemann surface. Proc. Japan Acad.36, 267–272 (1980). · Zbl 0102.29805 [7] M. Nakai, Order comparisons on canonical isomorphisms. Nagoya Math. J.50, 67–87 (1973). · Zbl 0271.31002 [8] M. Nakai, Uniform densities on hyperbolic Riemann surfaces. Nagoya Math. J.51, 1–24 (1973). · Zbl 0267.31009 [9] A. Osada, On the distribution of zeros of a strongly annular function. Nagoya Math. J.56, 13–17 (1974). · Zbl 0301.30025 [10] H.Royden, The equation{\(\Delta\)}u=Pu, and the classification of open Riemann surfaces. Ann. Acad. Sci. Fenn.271, 27 pp. (1959). · Zbl 0096.05803 [11] L.Sario and M.Nakai, Classification Theory of Riemann Surfaces. Berlin-Heidelberg-New York 1970. · Zbl 0199.40603 [12] T. Satō, Comparison theorems for Banach spaces of solutions of{\(\Delta\)}u=Pu on Riemann surfaces. J. Math. Soc. Japan31, 281–316 (1979). · Zbl 0397.31002 [13] M.Tsuji, Potential theory in modern function theory. Tokyo 1959. · Zbl 0087.28401 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.