Hostname: page-component-77c89778f8-sh8wx Total loading time: 0 Render date: 2024-07-16T18:35:28.352Z Has data issue: false hasContentIssue false
  • English
  • Français

Border Reduction in Existence Problems of Harmonic Forms

Published online by Cambridge University Press:  22 January 2016

Mitsuru Nakai  and
Leo Sario
Mitsuru Nakai
Affiliation:
Nagoya University and University of California, Los Angeles
Leo Sario
Affiliation:
Nagoya University and University of California, Los Angeles
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Given an arbitrary Riemannian n-space V let σ be a harmonic field in the complement V-V0 of a regular region V0. The problem of constructing in v a harmonic field ρ with the property was given a complete solution in [2]. The corresponding problem for harmonic forms σ, ρ remains open iri the general case. In the special case of locally flat spaces the construction can be carried out by replacing by the point norm [3].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 29 , March 1967 , pp. 137 - 143
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1967

References

[1] Duff, G.-Spencer, D., Harmonic tensors in Riemannian manifolds with boundary, Ann. of Math., 56 (1952), 128–156.CrossRefGoogle Scholar
[2] Nakai, M.-Sario, L., Harmonic fields with given boundary behavior in Riemannian spaces, J. Analyse Math, (to appear).Google Scholar
[3] Nakai, M.-Sario, L., Point norms in the construction of harmonic forms (to appear).Google Scholar
[4] Sario, L.-Schiffer, M.-Glasner, M., The span and principal functions in Riemannian spaces, J. Analyse Math. 15 (1965), 115–154.Google Scholar