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.
- Corneliu Constantinescu and Aurel Cornea, Ideale Ränder Riemannscher Flächen, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Band 32, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1963 (German). MR 0159935
- 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). MR 340633
- Carlo Miranda, Equazioni alle derivate parziali di tipo ellittico, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Heft 2, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1955 (Italian). MR 0087853
- M. Nakai and L. Sario, Biharmonic classification of Riemannian manifolds, Bull. Amer. Math. Soc. 77 (1971), 432–436. MR 278234, DOI https://doi.org/10.1090/S0002-9904-1971-12728-3
- L. Sario and M. Nakai, Classification theory of Riemann surfaces, Die Grundlehren der mathematischen Wissenschaften, Band 164, Springer-Verlag, New York-Berlin, 1970. MR 0264064
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Article copyright:
© Copyright 1972
American Mathematical Society
