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Harmonic spaces with positive potentials and nonconstant harmonic functions. (English) Zbl 0263.31011


MSC:

31A05 Harmonic, subharmonic, superharmonic functions in two dimensions
31B05 Harmonic, subharmonic, superharmonic functions in higher dimensions
31B15 Potentials and capacities, extremal length and related notions in higher dimensions
31A15 Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions
31D05 Axiomatic potential theory
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References:

[1] I. V. Anandam,Espaces Harmoniques Sans Potentiel Positif, Ann. Inst. Fourier, t. 22 (1972), (to appear). · Zbl 0235.31015
[2] Brelot, M., Lectures on Potential Theory (1960), Bombay: Tata Institute of Fundamental Research, Bombay · Zbl 0098.06903
[3] Brelot, M., Axiomatique des fonctions harmoniques, Cours d’été 1965 (1966), Montréal: Les Presses de l’Université, Montréal · Zbl 0148.10401
[4] C. Constantinescu and A. Cornea,Ideale Ränder Riemannscher Flächen, Ergeb. 32, Springer 1963. · Zbl 0112.30801
[5] Constantinescu, C.; Cornea, A., Compactifications of harmonic spaces, Nagoya Math. Journal, 25, 1-57 (1965) · Zbl 0138.36701
[6] Gowrisankaran, K., Fatou-Naim-Doob limit theorems in the axiomatic system of Brelot, Ann. Inst. Fourier, 16/2, 455-467 (1966) · Zbl 0145.15103
[7] Heins, M., On the principle of harmonic measure, comment, Math. Helv., 33, 47-58 (1959) · Zbl 0083.06903
[8] Hervé, Mme. R.-M., Recherches axiomatiques sur la théorie des fonctions surharmoniques et du potentiel, Ann. Inst. Fourier, 12, 415-571 (1962) · Zbl 0101.08103
[9] Nakai, M., Φbounded harmonic functions, Ann. Inst. Fourier, 16/1, 145-157 (1966) · Zbl 0154.36904
[10] L. Sario and M. Nakai,Classification Theory of Riemann Surfaces, Springer-Verlag, 1970. · Zbl 0199.40603
[11] B. Walsh,Flux in axiomatic potential Theory I, Inventiones Math., t. 8/3 (1969). · Zbl 0179.15203
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