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Bounded biharmonic functions on the Poincaré N-ball. (English) Zbl 0302.31010


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 functions on the Poincare iV-ball, J. Reine Angew. Math, (to appear). · Zbl 0269.31007
[2] D. HADA, L. SARIO AND C. WANG, iV-manif olds carrying bounded but no Di richlet 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 o Wiener’s and Royden’s compactifications, Ann. Inst. Fourier (Grenoble), 21 (1971), 217-226. · Zbl 0208.13703
[4] N. MIRSKY, L. SARIO AND C. WANG, Bounded polyharmonic functions and th dimension of the manifold, J. Math. Kyoto Univ., 13 (1973), 529-535. · Zbl 0284.31007
[5] M. NAKAI, Dirichlet finite biharmonic functions on the plane with distorte metrics, Nagoya Math. J., 51 (1973), 131-135. · Zbl 0268.31009
[6] M. NAKAI AND L. SARIO, Completeness and function-theoretic degeneracy o Riemannian spaces, Proc. Nat. Acad. Sci., 57 (1967), 29-31. · Zbl 0168.08903
[7] M. NAKAI AND L. SARIO, Biharmonic classification of Riemannian manifolds, Bull. Amer. Math. Soc, 77 (1971), 432-436 · Zbl 0253.31011
[8] M. NAKAI AND L. SARIO, Quasiharmonic classification of Riemannian manifolds, Proc. Amer. Math. Soc, 31 (1972), 165-169. · Zbl 0229.31006
[9] M. NAKAI AND L. SARIO, Dirichlet finite biharmonic functions with Dirichle finite Laplacians, Math. Z., 122 (1971), 203-216. · Zbl 0263.31006
[10] M. NAKAI AND L. SARIO, A property of biharmonic functions with Dirichle finite Laplacians, Math. Scand., 29 (1971), 307-316. · Zbl 0246.31009
[11] M. NAKAI AND L. SARIO, Existence of Dirichlet finite biharmonic functions, Ann. Acad. Sci. Fenn. A. I., 532 (1973), 1-33 · Zbl 0264.31008
[12] M. NAKAI AND L. SARIO, Existence of bounded biharmonic functions, J. Rein Angew. Math., 259 (1973), 147-156. · Zbl 0251.31003
[13] M. NAKAI AND L. SARIO, Existence of bounded Dirichlet finite biharmoni functions, Ann. Acad. Sci. Fenn. A. I., 505 (1972), 1-12. · Zbl 0236.31003
[14] M. NAKAI AND L. SARIO, Biharmonic functions on Riemannianmanifolds, Continuum Mechanics and Related Problems of Analysis, Nauka, Moscow, 1972, 329-335 · Zbl 0253.31004
[15] L. SARIO, Biharmonic and quasiharmonic functions on Riemannian manifolds, Duplicated lecture notes 1968-70, University of California, Los Angeles · Zbl 0302.31007
[16] L. SARIO, Quasiharmonic degeneracy of Riemannian iV-manif olds, Kdai Math Sem. Rep., 26 (1974), 53-57. · Zbl 0296.31011
[17] L. SARIO, Completeness and existence of bounded biharmonic functions on Riemannian manifold, Ann. Inst. Fourier (Grenoble), 24 (1974), 311-317. · Zbl 0273.31010
[18] L. SARIO AND M. NAKAI, Classification Theory of Riemann Surfaces, Springer Verlag, 1970, 446 pp. · Zbl 0199.40603
[19] L. SARIO AND C. WANG, The class of (p, q)-biharmonic functions, Pacific J. Math., 41 (1972), 799-808 · Zbl 0237.31013
[20] L. SARIO AND C. WANG, Counterexamples in the biharmonic classification o Riemannian 2-manifolds, Pacific J. Math., 50 (1974), 159-162. · Zbl 0252.31011
[21] L. SARIO AND C. WANG, Generators of the space of bounded biharmonic func tions, Math. Z., 127 (1972), 273-280. · Zbl 0217.10503
[22] L. SARIO AND C. WANG, Quasiharmonic functions on the Poincare -ball, Rend. Mat., 6 (1973), 1-14 · Zbl 0318.31011
[23] L. SARIO AND C. WANG, Riemannian manifolds of dimension ^4 withou bounded biharmonic functions, J. London Math. Soc, (2) 7 (1974), 635-644. · Zbl 0276.31007
[24] L. SARIO AND C. WANG, Existence of Dirichlet finite biharmonic functions o the Poincare 3-ball, Pacific J. Math., 48 (1973), 267-274. · Zbl 0242.31008
[25] L. SARIO AND C. WANG, Negative quasiharmonic functions, Thoku Math. J., 26 (1974), 85-93 · Zbl 0276.31005
[26] L. SARIO AND C. WANG, Radial quasiharmonic functions, Pacific J. Math., 46 (1973), 515-522 · Zbl 0256.31008
[27] L. SARIO AND C. WANG, Parabolicity and existence of bounded biharmoni functions, Comm. Math. Helv., 47 (1972), 341-347. · Zbl 0247.31012
[28] L. SARIO AND C. WANG, Positive harmonic functions and biharmonic degen eracy, Bull. Amer. Math. Soc, 79 (1973), 182-187. · Zbl 0252.31010
[29] L. SARIO AND C. WANG, Parabolicity and existence of Dirichlet finite bi harmonic functions, J. London Math. Soc, (2) 8 (1974), 145-148. · Zbl 0278.31009
[30] L. SARIO AND C. WANG, Harmonic and biharmonic degeneracy, Kdai Math Sem. Rep., 25 (1973), 392-396. · Zbl 0272.31005
[31] L. SARIO AND C. WANG, Harmonic /^-functionson Riemannianmanifolds, Kdai Math. Sem. Rep., 26 (1975), 204-209 · Zbl 0302.31007
[32] L. SARIO, C. WANG AND M. RANGE, Biharmonic projection and decomposition, Ann. Acad. Sci. Fenn. A. I., 494 (1971), 1-14 · Zbl 0219.31007
[33] C. WANG AND L. SARIO, Polyharmonic classification of Riemannian manifolds, J. Math. Kyoto Univ., 12 (1972), 129-140 · Zbl 0227.31008
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