Riemannian manifolds with bounded Dirichlet finite polyharmonic functions
Lung Ock Chung, Leo Sario, Cecilia Wang (1973)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Lung Ock Chung, Leo Sario, Cecilia Wang (1973)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Leo Sario (1974)
Annales de l'institut Fourier
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A.S. Galbraith has communicated to us the following intriguing problem: does the completeness of a manifold imply, or is it implied by, the emptiness of the class of bounded nonharmonic biharmonic functions? Among all manifolds considered thus far in biharmonic classification theory (cf. Bibliography), those that are complete fail to carry -functions, and one might suspect that this is always the case. We shall show, however, that there do exist complete manifolds of any dimension...
Mitsuru Nakai, Leo Sario (1976)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Fuglede, Bent (1996)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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Stere Ianuş, Gabriel Eduard Vîlcu, Rodica Cristina Voicu (2011)
Banach Center Publications
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It is well known that Riemannian submersions are of interest in physics, owing to their applications in the Yang-Mills theory, Kaluza-Klein theory, supergravity and superstring theories. In this paper we give a survey of harmonic maps and Riemannian submersions between manifolds equipped with certain geometrical structures such as almost Hermitian structures, contact structures, f-structures and quaternionic structures. We also present some new results concerning holomorphic maps and...
Hong Min-Chun (1992)
Manuscripta mathematica
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Robert E. Greene, H. Wu (1975)
Annales de l'institut Fourier
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Let be a noncompact Riemannian manifold of dimension . Then there exists a proper embedding of into by harmonic functions on . It is easy to find harmonic functions which give an embedding. However, it is more difficult to achieve properness. The proof depends on the theorems of Lax-Malgrange and Aronszajn-Cordes in the theory of elliptic equations.