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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
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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