Displaying similar documents to “Riemannian manifolds with bounded Dirichlet finite polyharmonic functions”

Completeness and existence of bounded biharmonic functions on a riemannian manifold

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 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...

Convergence of Riemannian manifolds and Laplace operators. I

Atsushi Kasue (2002)

Annales de l’institut Fourier

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We study the spectral convergence of compact Riemannian manifolds in relation with the Gromov-Hausdorff distance and discuss the geodesic distances and the energy forms of the limit spaces.

Harmonic maps and Riemannian submersions between manifolds endowed with special structures

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...