Displaying similar documents to “Completeness and existence of bounded biharmonic functions on a riemannian manifold”

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.

Modular Classes of Q-Manifolds, Part II: Riemannian Structures & Odd Killing Vectors Fields

Andrew James Bruce (2020)

Archivum Mathematicum

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We define and make an initial study of (even) Riemannian supermanifolds equipped with a homological vector field that is also a Killing vector field. We refer to such supermanifolds as Riemannian Q-manifolds. We show that such Q-manifolds are unimodular, i.e., come equipped with a Q-invariant Berezin volume.

Behavior of biharmonic functions on Wiener's and Royden's compactifications

Y. K. Kwon, Leo Sario, Bertram Walsh (1971)

Annales de l'institut Fourier

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Let R be a smooth Riemannian manifold of finite volume, Δ its Laplace (-Beltrami) operator. Canonical direct-sum decompositions of certain subspaces of the Wiener and Royden algebras of R are found, and for biharmonic functions (those for which Δ Δ u = 0 ) the decompositions are related to the values of the functions and their Laplacians on appropriate ideal boundaries.