Some Progress in Conformal Geometry
This is a survey paper of our current research on the theory of partial differential equations in conformal geometry. Our intention is to describe some of our current works in a rather brief and expository fashion. We are not giving a comprehensive survey on the subject and references cited here are...
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| Datum: | 2007 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2007
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/147215 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Some Progress in Conformal Geometry / Sun-Yung A. Chang, J. Qing, P. Yang // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 15 назв. — англ. |
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irk-123456789-1472152019-02-14T01:26:02Z Some Progress in Conformal Geometry Sun-Yung A. Chang Qing, J. Yang, P. This is a survey paper of our current research on the theory of partial differential equations in conformal geometry. Our intention is to describe some of our current works in a rather brief and expository fashion. We are not giving a comprehensive survey on the subject and references cited here are not intended to be complete. We introduce a bubble tree structure to study the degeneration of a class of Yamabe metrics on Bach flat manifolds satisfying some global conformal bounds on compact manifolds of dimension 4. As applications, we establish a gap theorem, a finiteness theorem for diffeomorphism type for this class, and diameter bound of the σ2-metrics in a class of conformal 4-manifolds. For conformally compact Einstein metrics we introduce an eigenfunction compactification. As a consequence we obtain some topological constraints in terms of renormalized volumes. 2007 Article Some Progress in Conformal Geometry / Sun-Yung A. Chang, J. Qing, P. Yang // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 15 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 53A30; 53C20; 35J60 http://dspace.nbuv.gov.ua/handle/123456789/147215 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
This is a survey paper of our current research on the theory of partial differential equations in conformal geometry. Our intention is to describe some of our current works in a rather brief and expository fashion. We are not giving a comprehensive survey on the subject and references cited here are not intended to be complete. We introduce a bubble tree structure to study the degeneration of a class of Yamabe metrics on Bach flat manifolds satisfying some global conformal bounds on compact manifolds of dimension 4. As applications, we establish a gap theorem, a finiteness theorem for diffeomorphism type for this class, and diameter bound of the σ2-metrics in a class of conformal 4-manifolds. For conformally compact Einstein metrics we introduce an eigenfunction compactification. As a consequence we obtain some topological constraints in terms of renormalized volumes. |
| format |
Article |
| author |
Sun-Yung A. Chang Qing, J. Yang, P. |
| spellingShingle |
Sun-Yung A. Chang Qing, J. Yang, P. Some Progress in Conformal Geometry Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Sun-Yung A. Chang Qing, J. Yang, P. |
| author_sort |
Sun-Yung A. Chang |
| title |
Some Progress in Conformal Geometry |
| title_short |
Some Progress in Conformal Geometry |
| title_full |
Some Progress in Conformal Geometry |
| title_fullStr |
Some Progress in Conformal Geometry |
| title_full_unstemmed |
Some Progress in Conformal Geometry |
| title_sort |
some progress in conformal geometry |
| publisher |
Інститут математики НАН України |
| publishDate |
2007 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147215 |
| citation_txt |
Some Progress in Conformal Geometry / Sun-Yung A. Chang, J. Qing, P. Yang // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 15 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT sunyungachang someprogressinconformalgeometry AT qingj someprogressinconformalgeometry AT yangp someprogressinconformalgeometry |
| first_indexed |
2025-07-11T01:38:29Z |
| last_indexed |
2025-07-11T01:38:29Z |
| _version_ |
1837312681552379904 |