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Quasiharmonic functions on the Poincaré N-ball. (English) Zbl 0271.31004


MSC:

31B30 Biharmonic and polyharmonic equations and functions in higher dimensions
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[1] D. Hada, L. Sario, and C. Wang, Dirichlet finite biharmonic function on the Poincaré \?-ball, J. Reine Angew. Math. 272 (1974), 92 – 101. · Zbl 0269.31007 · doi:10.1090/S0002-9904-1973-13257-4
[2] Dennis Hada, Leo Sario, and Cecilia Wang, \?-manifolds carrying bounded but no Dirichlet finite harmonic functions, Nagoya Math J. 54 (1974), 1 – 6. · Zbl 0264.31004
[3] Y. K. Kwon, L. Sario, and B. Walsh, Behavior of biharmonic functions on Wiener’s and Royden’s compactifications, Ann. Inst. Fourier (Grenoble) 21 (1971), no. 3, 217 – 226 (English, with French summary). · Zbl 0208.13703
[4] Mitsuru Nakai and Leo Sario, A parabolic Riemannian ball, Entire Functions and Related Parts of Analysis (Proc. Sympos. Pure Math., La Jolla, Calif., 1966) Amer. Math. Soc., Providence, R.I., 1968, pp. 341 – 349. · Zbl 0173.13901
[5] Mitsuru Nakai and Leo Sario, Quasiharmonic classification of Riemannian manifolds, Proc. Amer. Math. Soc. 31 (1972), 165 – 169. · Zbl 0229.31006
[6] Mitsuru Nakai and Leo Sario, Existence of Dirichlet finite biharmonic functions, Ann. Acad. Sci. Fenn. Ser. AI . 532 (1973), 34. · Zbl 0264.31008
[7] Mitsuru Nakai and Leo Sario, Existence of bounded biharmonic functions, J. Reine Angew. Math. 259 (1973), 147 – 156. · Zbl 0251.31003
[8] L. Sario, Biharmonic and quasiharmonic functions on Riemannian manifolds, Duplicated lecture notes 1969-1970, University of California, Los Angeles, Calif.
[9] Leo Sario and Cecilia Wang, Quasiharmonic functions on the Poincaré \?-ball, Bull. Amer. Math. Soc. 79 (1973), 922 – 923. · Zbl 0256.31008
[10] Leo Sario and Cecilia Wang, Radial quasiharmonic functions, Pacific J. Math. 46 (1973), 515 – 522. · Zbl 0256.31008
[11] Leo Sario and Cecilia Wang, Negative quasiharmonic functions, Tôhoku Math. J. (2) 26 (1974), 85 – 93. · Zbl 0276.31005 · doi:10.2748/tmj/1178241237
[12] Leo Sario and Cecilia Wang, Parabolicity and existence of bounded biharmonic functions, Comment. Math. Helv. 47 (1972), 341 – 347. · Zbl 0247.31012 · doi:10.1007/BF02566809
[13] Leo Sario and Cecilia Wang, Parabolicity and existence of Dirichlet finite biharmonic functions, J. London Math. Soc. (2) 8 (1974), 145 – 148. · Zbl 0278.31009 · doi:10.1112/jlms/s2-8.1.145
[14] Leo Sario and Cecilia Wang, Existence of Dirichlet finite biharmonic functions on the Poincaré 3-ball, Pacific J. Math. 48 (1973), 267 – 274. · Zbl 0242.31008
[15] Leo Sario and Cecilia Wang, Positive harmonic functions and biharmonic degeneracy, Bull. Amer. Math. Soc. 79 (1973), 182 – 187. · Zbl 0252.31010
[16] Leo Sario and Cecilia Wang, Harmonic and biharmonic degeneracy, Kōdai Math. Sem. Rep. 25 (1973), 392 – 396. · Zbl 0272.31005
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