An extension of the Denjoy-Carleman-Ahlfors theorem in subharmonic form

Skeath, J. E.

doi:10.1090/S0002-9947-1965-0185114-X

An extension of the Denjoy-Carleman-Ahlfors theorem in subharmonic form
HTML articles powered by AMS MathViewer

by J. E. Skeath

Trans. Amer. Math. Soc. 119 (1965), 535-551

DOI: https://doi.org/10.1090/S0002-9947-1965-0185114-X

PDF | Request permission

References

Lars V. Ahlfors and Leo Sario, Riemann surfaces, Princeton Mathematical Series, No. 26, Princeton University Press, Princeton, N.J., 1960. MR 0114911

Sur une inégalité différentielle dans la théorie des fonctions analytiques

196

Corneliu Constantinescu and Aurel Cornea, Über einige Probleme von M. Heins, Rev. Math. Pures Appl. 4 (1959), 277–281 (German). MR 113997
Aurel Cornea, Über eine Formel in der Extremisierungstheorie, Rev. Math. Pures Appl. 3 (1958), 431–436 (German). MR 108583
Alexander Dinghas, Vorlesungen über Funktionentheorie, Die Grundlehren der mathematischen Wissenschaften, Band 110, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1961 (German). MR 0179329
Griffith C. Evans, Potentials and positively infinite singularities of harmonic functions, Monatsh. Math. Phys. 43 (1936), no. 1, 419–424. MR 1550546, DOI 10.1007/BF01707623
Maurice Heins, Riemann surfaces of infinite genus, Ann. of Math. (2) 55 (1952), 296–317. MR 45834, DOI 10.2307/1969780
Maurice Heins, Asymptotic spots of entire and meromorphic functions, Ann. of Math. (2) 66 (1957), 430–439. MR 94457, DOI 10.2307/1969900
Maurice Heins, On a notion of convexity connected with a method of Carleman, J. Analyse Math. 7 (1959), 53–77. MR 114000, DOI 10.1007/BF02787680
Maurice Heins, Selected topics in the classical theory of functions of a complex variable, Athena Series: Selected Topics in Mathematics, Holt, Rinehart and Winston, New York, 1962. MR 0162913
Bo Kjellberg, On the growth of minimal positive harmonic functions in a plane region, Ark. Mat. 1 (1950), 347–351. MR 38499, DOI 10.1007/BF02591371
Zenjiro Kuramochi, An example of a null-boundary Riemann surface, Osaka Math. J. 6 (1954), 83–91. MR 64150
Zenjiro Kuramochi, Evans’s theorem on abstract Riemann surfaces with null-boundaries. I, II, Proc. Japan Acad. 32 (1956), 1–6, 7–9. MR 77652
Zenjiro Kuramochi, Mass distributions on the ideal boundaries of abstract Riemann surfaces. I, Osaka Math. J. 8 (1956), 119–137. MR 79638
Robert S. Martin, Minimal positive harmonic functions, Trans. Amer. Math. Soc. 49 (1941), 137–172. MR 3919, DOI 10.1090/S0002-9947-1941-0003919-6
Mitsuru Nakai, On Evans potential, Proc. Japan Acad. 38 (1962), 624–629. MR 150296
Rolf Nevanlinna, Uniformisierung, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, Band LXIV, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1953 (German). MR 0057335
George Springer, Introduction to Riemann surfaces, Addison-Wesley Publishing Co., Inc., Reading, Mass., 1957. MR 0092855