Biharmonic extensions in Riemannian manifolds
type: Item
instance of: scholarly article
title: Biharmonic extensions in Riemannian manifolds
zbMATH Open document ID: 0952.31006
author: Victor Anandam
author: I. Bajunaid
published in: Hiroshima Mathematical Journal
publication date: 2000-12-28T00:00:00Z
review text: Let \(R\) be a hyperbolic Riemannian manifold. It is known that given a harmonic function \(h\) outside a compact set, there always exists a harmonic function \(H\) on \(R\) such that \(H-h\) is bounded outside a compact set. The authors prove that a biharmonic extension in \(R\) is possible if and only if there exist potentials \(p>0\) and \(q>0\) in \(R\) (\(q\) is bounded outside a compact set) such that \(\Delta q=p\), where \(\Delta \) is the Laplace-Beltrami operator in \(R\).
Mathematics Subject Classification ID: 31C12
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 1484782
zbMATH Keywords: tapered manifold
zbMATH Keywords: biharmonic extension
reviewed by: Vladimir Mityushev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1484782