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Quasiharmonic classification of Riemannian manifolds


Authors: Mitsuru Nakai and Leo Sario
Journal: Proc. Amer. Math. Soc. 31 (1972), 165-169
DOI: https://doi.org/10.1090/S0002-9939-1972-0287488-7
MathSciNet review: 0287488
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Abstract | References | Additional Information

Abstract: In the study of the structure of the space of biharmonic functions it is often necessary to impose some nondegeneracy condition on the base manifold with respect to quasiharmonic functions (cf. [2], [4]). For this reason it is useful to introduce various quasiharmonically degenerate classes of Riemannian manifolds and to investigate relations among them. This is the purpose of the present note.


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  • [1] C. Constantinescu and A. Cornea, Ideale Ränder Riemannscher Flächen, Ergebnisse der Mathematik und ihrer Grenzgebiete, Heft 32, Springer-Verlag, Berlin, 1963. MR 28 #3151. MR 0159935 (28:3151)
  • [2] Y. K. Kwon, L. Sario and B. Walsh, Behavior of biharmonic functions on Wiener's and Royden's compactifications, Ann. Inst. Fourier (Grenoble) (to appear). MR 0340633 (49:5385)
  • [3] C. Miranda, Equazioni alle derivate parziali di tipo ellittico, Ergebnisse der Mathematik und ihrer Grenzgebiete, Heft 2, Springer-Verlag, Berlin, 1955; English transl., Springer-Verlag, Berlin, 1970. MR 19, 421. MR 0087853 (19:421d)
  • [4] M. Nakai and L. Sario, Biharmonic classification of Riemannian manifolds, Bull. Amer. Math. Soc. 77 (1971), 432-436. MR 0278234 (43:3965)
  • [5] L. Sario and M. Nakai, Classification theory of Riemann surfaces, Die Grundlehren der math. Wissenschaften, Band 164, Springer-Verlag, Berlin and New York, 1970. MR 0264064 (41:8660)


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0287488-7
Article copyright: © Copyright 1972 American Mathematical Society

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