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 |
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| Format: | Artikel |
| Sprache: | English |
| 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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Fox, D. 2019-02-19T17:36:22Z 2019-02-19T17:36:22Z 2009 Boundaries of Graphs of Harmonic Functions / D. Fox // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 8 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 35J05; 35J25; 53B25 https://nasplib.isofts.kiev.ua/handle/123456789/149134 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. This paper is a contribution to the Special Issue “Elie Cartan and Differential Geometry”. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Boundaries of Graphs of Harmonic Functions Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Boundaries of Graphs of Harmonic Functions |
| spellingShingle |
Boundaries of Graphs of Harmonic Functions Fox, D. |
| title_short |
Boundaries of Graphs of Harmonic Functions |
| title_full |
Boundaries of Graphs of Harmonic Functions |
| title_fullStr |
Boundaries of Graphs of Harmonic Functions |
| title_full_unstemmed |
Boundaries of Graphs of Harmonic Functions |
| title_sort |
boundaries of graphs of harmonic functions |
| author |
Fox, D. |
| author_facet |
Fox, D. |
| publishDate |
2009 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/149134 |
| citation_txt |
Boundaries of Graphs of Harmonic Functions / D. Fox // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 8 назв. — англ. |
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AT foxd boundariesofgraphsofharmonicfunctions |
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2025-12-07T15:17:19Z |
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2025-12-07T15:17:19Z |
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1850863139927621632 |