Boundaries of Graphs of Harmonic Functions
Harmonic functions u: Rn → Rm are equivalent to integral manifolds of an exterior differential system with independence condition (M,I,ω). To this system one associates the space of conservation laws C. They provide necessary conditions for g: Sn–1 → M to be the boundary of an integral submanifold....
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2009 |
| ISSN: | 1815-0659 |
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| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2009
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149134 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Boundaries of Graphs of Harmonic Functions / D. Fox // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 8 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | Harmonic functions u: Rn → Rm are equivalent to integral manifolds of an exterior differential system with independence condition (M,I,ω). To this system one associates the space of conservation laws C. They provide necessary conditions for g: Sn–1 → M to be the boundary of an integral submanifold. We show that in a local sense these conditions are also sufficient to guarantee the existence of an integral manifold with boundary g(Sn–1). The proof uses standard linear elliptic theory to produce an integral manifold G: Dn → M and the completeness of the space of conservation laws to show that this candidate has g(Sn–1) as its boundary. As a corollary we obtain a new elementary proof of the characterization of boundaries of holomorphic disks in Cm in the local case.
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| ISSN: | 1815-0659 |