Displaying similar documents to “Quasiharmonic L p -functions on riemannian manifolds”

Completeness and existence of bounded biharmonic functions on a riemannian manifold

Leo Sario (1974)

Annales de l'institut Fourier

Similarity:

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 H 2 B of bounded nonharmonic biharmonic functions? Among all manifolds considered thus far in biharmonic classification theory (cf. Bibliography), those that are complete fail to carry H 2 B -functions, and one might suspect that this is always the case. We shall show, however, that there do exist complete manifolds of any dimension...

Harmonic maps and Riemannian submersions between manifolds endowed with special structures

Stere Ianuş, Gabriel Eduard Vîlcu, Rodica Cristina Voicu (2011)

Banach Center Publications

Similarity:

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...

Embedding of open riemannian manifolds by harmonic functions

Robert E. Greene, H. Wu (1975)

Annales de l'institut Fourier

Similarity:

Let M be a noncompact Riemannian manifold of dimension n . Then there exists a proper embedding of M into R 2 n + 1 by harmonic functions on M . It is easy to find 2 n + 1 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.