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Border Reduction in Existence Problems of Harmonic Forms

  • Mitsuru Nakai (a1) and Leo Sario (a1)
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Given an arbitrary Riemannian n-space V let σ be a harmonic field in the complement V-V 0 of a regular region V 0. 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].

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References
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[1] Duff, G.-Spencer, D., Harmonic tensors in Riemannian manifolds with boundary, Ann. of Math., 56 (1952), 128156.
[2] Nakai, M.-Sario, L., Harmonic fields with given boundary behavior in Riemannian spaces, J. Analyse Math, (to appear).
[3] Nakai, M.-Sario, L., Point norms in the construction of harmonic forms (to appear).
[4] Sario, L.-Schiffer, M.-Glasner, M., The span and principal functions in Riemannian spaces, J. Analyse Math. 15 (1965), 115154.
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Nagoya Mathematical Journal
  • ISSN: 0027-7630
  • EISSN: 2152-6842
  • URL: /core/journals/nagoya-mathematical-journal
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