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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2009 |
| Main Author: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2009
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149134 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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| _version_ | 1862665350859980800 |
|---|---|
| author | Fox, D. |
| author_facet | Fox, D. |
| citation_txt | Boundaries of Graphs of Harmonic Functions / D. Fox // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 8 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T15:17:19Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149134 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T15:17:19Z |
| publishDate | 2009 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | Boundaries of Graphs of Harmonic Functions Fox, D. |
| title | 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_short | Boundaries of Graphs of Harmonic Functions |
| title_sort | boundaries of graphs of harmonic functions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149134 |
| work_keys_str_mv | AT foxd boundariesofgraphsofharmonicfunctions |